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What Is the Rule for Drawing Free-body Diagram

Written By Friday, April 8, 2022 Add Comment Edit

Learning Objectives

Past the end of the department, you will be able to:

  • Explain the rules for cartoon a free-torso diagram
  • Construct free-body diagrams for different situations

The get-go step in describing and analyzing near phenomena in physics involves the careful drawing of a free-body diagram. Free-body diagrams accept been used in examples throughout this affiliate. Remember that a free-body diagram must simply include the external forces interim on the body of involvement. Once nosotros have drawn an authentic gratuitous-trunk diagram, nosotros tin apply Newton's first law if the body is in equilibrium (balanced forces; that is, [latex] {F}_{\text{net}}=0 [/latex]) or Newton's second law if the trunk is accelerating (unbalanced force; that is, [latex] {F}_{\text{cyberspace}}\ne 0 [/latex]).

In Forces, we gave a cursory problem-solving strategy to help you understand free-trunk diagrams. Here, nosotros add some details to the strategy that will assistance you in amalgam these diagrams.

Problem-Solving Strategy: Constructing Free-Body Diagrams

Notice the following rules when amalgam a costless-torso diagram:

  1. Draw the object nether consideration; it does not have to exist artistic. At first, you may desire to draw a circle around the object of involvement to exist sure you focus on labeling the forces acting on the object. If you are treating the object as a particle (no size or shape and no rotation), stand for the object as a point. Nosotros often place this bespeak at the origin of an xy-coordinate arrangement.
  2. Include all forces that human activity on the object, representing these forces equally vectors. Consider the types of forces described in Common Forces—normal force, friction, tension, and bound force—too as weight and applied force. Do not include the cyberspace force on the object. With the exception of gravity, all of the forces we have discussed crave directly contact with the object. However, forces that the object exerts on its surround must not be included. Nosotros never include both forces of an activity-reaction pair.
  3. Catechumen the costless-body diagram into a more detailed diagram showing the ten– and y-components of a given force (this is oftentimes helpful when solving a problem using Newton's first or 2d law). In this case, place a squiggly line through the original vector to testify that information technology is no longer in play—it has been replaced by its x– and y-components.
  4. If there are ii or more than objects, or bodies, in the trouble, draw a separate complimentary-body diagram for each object.

Note: If at that place is dispatch, we exercise non direct include it in the complimentary-body diagram; however, information technology may assist to indicate acceleration outside the free-body diagram. Y'all can label it in a dissimilar color to indicate that it is dissever from the free-body diagram.

Let's employ the trouble-solving strategy in drawing a free-torso diagram for a sled. In (Figure)(a), a sled is pulled past force P at an angle of [latex] 30\text{°} [/latex]. In part (b), we show a gratis-body diagram for this state of affairs, as described by steps 1 and 2 of the problem-solving strategy. In part (c), nosotros show all forces in terms of their x– and y-components, in keeping with pace 3.

Figure a shows a sled of 15 kg. An arrow labeled P pointing right and up forms an angle of 30 degrees with the horizontal. Figure b is a free body diagram with P, N pointing up and w pointing down. Figure c is a free body diagram with P, N, w and two components of P: Px pointing right and Py pointing up.

Effigy 5.31 (a) A moving sled is shown as (b) a gratuitous-trunk diagram and (c) a gratis-body diagram with force components.

Example

Two Blocks on an Inclined Plane

Construct the free-body diagram for object A and object B in (Figure).

Strategy

We follow the four steps listed in the trouble-solving strategy.

Solution

We showtime past creating a diagram for the kickoff object of interest. In (Figure)(a), object A is isolated (circled) and represented past a dot.

Figure a shows two objects on an inclined plane, sloping down to the left. Object A is on top of object B. A free body diagram shows T pointing right and up, parallel to the plane, N subscript BA pointing left and up, perpendicular to the plane, f subscript BA pointing left and down, parallel to the plane and w subscript A pointing vertically down. W subscript A is weight of block A, T is tension, N subscript BA is normal force exerted by B on A, f subscript BA is friction force exerted by B on A. Figure b shows the objects on the slope in the same manner. A free body diagram has f subscript B and f subscript AB pointing right and up, parallel to the slope, N subscript B pointing left and up perpendicular to the slope, w subscript B pointing vertically down and N subscript AB pointing down and right, perpendicular to the slope. W subscript B is weight of block B, N subscript AB is normal force exerted by A on B, N subscript B is normal force exerted by the incline plane on B. f subscript AB is friction force exerted by A on B. f subscript B is friction force exerted by the incline plane on B.

Figure 5.32 (a) The gratis-torso diagram for isolated object A. (b) The free-torso diagram for isolated object B. Comparing the 2 drawings, we meet that friction acts in the opposite direction in the two figures. Considering object A experiences a force that tends to pull it to the right, friction must human activity to the left. Because object B experiences a component of its weight that pulls it to the left, down the incline, the friction force must oppose it and deed up the ramp. Friction ever acts contrary the intended direction of motion.

We now include any force that acts on the body. Hither, no applied force is present. The weight of the object acts as a force pointing vertically down, and the presence of the cord indicates a forcefulness of tension pointing abroad from the object. Object A has one interface and hence experiences a normal force, directed away from the interface. The source of this force is object B, and this normal force is labeled accordingly. Since object B has a tendency to slide downward, object A has a tendency to slide up with respect to the interface, so the friction [latex] {f}_{\text{BA}} [/latex] is directed downwardly parallel to the inclined airplane.

As noted in footstep four of the problem-solving strategy, nosotros then construct the gratis-body diagram in (Figure)(b) using the same approach. Object B experiences two normal forces and 2 friction forces due to the presence of ii contact surfaces. The interface with the inclined airplane exerts external forces of [latex] {Northward}_{\text{B}} [/latex] and [latex] {f}_{\text{B}} [/latex], and the interface with object B exerts the normal force [latex] {N}_{\text{AB}} [/latex] and friction [latex] {f}_{\text{AB}} [/latex]; [latex] {North}_{\text{AB}} [/latex] is directed away from object B, and [latex] {f}_{\text{AB}} [/latex] is opposing the tendency of the relative motion of object B with respect to object A.

Significance

The object nether consideration in each part of this trouble was circled in grayness. When you are first learning how to depict free-trunk diagrams, you volition observe it helpful to circumvolve the object before deciding what forces are acting on that item object. This focuses your attention, preventing y'all from because forces that are not acting on the body.

Instance

Two Blocks in Contact

A force is applied to two blocks in contact, as shown.

Strategy

Draw a free-body diagram for each block. Exist certain to consider Newton's 3rd police force at the interface where the 2 blocks touch.

Two squares are shown in contact with each other. The left one is smaller and is labeled m1. The right one is bigger and is labeled m2. An arrow pointing right towards m1 is labeled F.

Solution

Figure shows two free body diagrams. The first one shows arrow A subscript 21 pointing left and arrow F pointing right. The second one shows arrow A 12 pointing right. Both diagrams also have arrows pointing up and down.

Significance[latex] {\overset{\to }{A}}_{21} [/latex] is the action strength of block 2 on block ane. [latex] {\overset{\to }{A}}_{12} [/latex] is the reaction force of block i on cake two. We use these free-body diagrams in Applications of Newton's Laws.

Case

Block on the Table (Coupled Blocks)

A cake rests on the table, as shown. A light rope is attached to it and runs over a pulley. The other end of the rope is attached to a 2d block. The two blocks are said to exist coupled. Block [latex] {m}_{2} [/latex] exerts a strength due to its weight, which causes the system (two blocks and a cord) to accelerate.

Strategy

We presume that the string has no mass so that we do not have to consider it as a separate object. Depict a free-body diagram for each block.

Figure shows block m1 placed on a table. A string attached to it runs over a pulley and down the right side of the table. A block m2 is suspended from it. An arrow a1 points right and an arrow a2 points down.

Solution

Figure a shows block m1. An arrow labeled m1g point upwards from it, an arrow N points downwards and an arrow T points right. Figure b shows block m2. An arrow T points upwards from it and an arrow m2g points downwards.

Significance

Each cake accelerates (discover the labels shown for [latex] {\overset{\to }{a}}_{1} [/latex] and [latex] {\overset{\to }{a}}_{2} [/latex]); however, assuming the cord remains taut, they accelerate at the same rate. Thus, we have [latex] {\overset{\to }{a}}_{ane}={\overset{\to }{a}}_{2} [/latex]. If we were to go along solving the problem, nosotros could simply phone call the acceleration [latex] \overset{\to }{a} [/latex]. Too, we use two free-torso diagrams because we are unremarkably finding tension T, which may require u.s. to use a system of two equations in this type of problem. The tension is the aforementioned on both [latex] {g}_{1}\,\text{and}\,{thousand}_{2} [/latex].

Check Your Agreement

(a) Describe the costless-body diagram for the situation shown. (b) Redraw it showing components; use ten-axes parallel to the two ramps.

Two carts are tied with a rope which goes over a pulley on top of a hill. Each cart rests on one slope of the hill on either side of the pulley. The cart on the left is labeled m1 and the one on the right is labeled m2.

Effigy a shows a free body diagram of an object on a line that slopes down to the correct. Arrow T from the object points correct and up, parallel to the slope. Pointer N1 points left and up, perpendicular to the slope. Arrow w1 points vertically down. Arrow w1x points left and down, parallel to the slope. Arrow w1y points right and down, perpendicular to the gradient. Figure b shows a free trunk diagram of an object on a line that slopes downwardly to the left. Arrow N2 from the object points right and up, perpendicular to the slope. Arrow T points left and up, parallel to the slope. Pointer w2 points vertically down. Arrow w2y points left and downward, perpendicular to the gradient. Arrow w2x points right and down, parallel to the gradient.

View this simulation to predict, qualitatively, how an external force will impact the speed and direction of an object's motion. Explain the effects with the help of a costless-trunk diagram. Use free-body diagrams to draw position, velocity, acceleration, and force graphs, and vice versa. Explain how the graphs chronicle to 1 another. Given a scenario or a graph, sketch all four graphs.

Summary

  • To draw a free-body diagram, we draw the object of involvement, draw all forces acting on that object, and resolve all strength vectors into x– and y-components. We must draw a carve up free-trunk diagram for each object in the problem.
  • A gratis-torso diagram is a useful means of describing and analyzing all the forces that act on a body to make up one's mind equilibrium co-ordinate to Newton'due south beginning police force or acceleration according to Newton'southward 2d law.

Cardinal Equations

Cyberspace external force [latex] {\overset{\to }{F}}_{\text{net}}=\sum \overset{\to }{F}={\overset{\to }{F}}_{ane}+{\overset{\to }{F}}_{2}+\text{⋯} [/latex]
Newton'due south first law [latex] \overset{\to }{v}=\,\text{constant when}\,{\overset{\to }{F}}_{\text{internet}}=\overset{\to }{0}\,\text{N} [/latex]
Newton's 2nd law, vector class [latex] {\overset{\to }{F}}_{\text{net}}=\sum \overset{\to }{F}=k\overset{\to }{a} [/latex]
Newton'due south second constabulary, scalar form [latex] {F}_{\text{net}}=ma [/latex]
Newton'due south 2d law, component form [latex] \sum {\overset{\to }{F}}_{x}=k{\overset{\to }{a}}_{ten}\text{,}\,\sum {\overset{\to }{F}}_{y}=m{\overset{\to }{a}}_{y},\,\text{and}\,\sum {\overset{\to }{F}}_{z}=m{\overset{\to }{a}}_{z}. [/latex]
Newton's second law, momentum class [latex] {\overset{\to }{F}}_{\text{cyberspace}}=\frac{d\overset{\to }{p}}{dt} [/latex]
Definition of weight, vector course [latex] \overset{\to }{w}=m\overset{\to }{g} [/latex]
Definition of weight, scalar form [latex] w=mg [/latex]
Newton's third police [latex] {\overset{\to }{F}}_{\text{AB}}=\text{−}{\overset{\to }{F}}_{\text{BA}} [/latex]
Normal force on an object resting on a

horizontal surface, vector form

 [latex] \overset{\to }{N}=\text{−}chiliad\overset{\to }{g} [/latex]
Normal force on an object resting on a

horizontal surface, scalar form

 [latex] N=mg [/latex]
Normal strength on an object resting on an

inclined airplane, scalar form

 [latex] North=mg\text{cos}\,\theta [/latex]
Tension in a cable supporting an object

of mass m at residual, scalar grade

 [latex] T=w=mg [/latex]

Conceptual Questions

In completing the solution for a problem involving forces, what do we do afterwards amalgam the free-body diagram? That is, what do we utilize?

If a book is located on a table, how many forces should be shown in a free-trunk diagram of the volume? Describe them.

Ii forces of different types: weight acting downward and normal force acting upward

If the book in the previous question is in gratis fall, how many forces should be shown in a free-body diagram of the book? Depict them.

Issues

A brawl of mass grand hangs at residue, suspended by a cord. (a) Sketch all forces. (b) Draw the gratuitous-body diagram for the ball.

A automobile moves along a horizontal road. Draw a free-body diagram; exist sure to include the friction of the route that opposes the forward motion of the motorcar.

A free body diagram shows a vector F subscript e pointing right, vector N pointing up, vector f pointing left and arrow w pointing down.

A runner pushes against the rails, as shown. (a) Provide a free-trunk diagram showing all the forces on the runner. (Hint: Place all forces at the centre of his body, and include his weight.) (b) Give a revised diagram showing the xy-component form.

A picture of a man running towards the right is shown. An arrow labeled F points up and right from the floor towards his foot.

The traffic light hangs from the cables as shown. Draw a free-body diagram on a coordinate airplane for this situation.

Figure shows a traffic light hanging from a horizontal cable by three other cables, T1, T2 and T3. T1 hangs down and right making an angle of 41 degrees with the horizontal cable. T2 hangs down and left, making an angle of 63 degrees with the horizontal cable. These meet at a point and T3 hangs vertically down from here. The light is attached to T3. A vector pointing down from the light is labeled w equal to 200 newtons.

Figure shows coordinate axes. Three arrows radiate out from the origin. T1, labeled 41 degrees points up and left. T2, labeled 63 degrees points up and right. T3 equal to w equal to 200 N is along the negative y axis.

Boosted Issues

Two small forces, [latex] {\overset{\to }{F}}_{1}=-two.xl\hat{i}-vi.10t\hat{j} [/latex] North and [latex] {\overset{\to }{F}}_{2}=eight.50\lid{i}-9.seventy\hat{j} [/latex] N, are exerted on a rogue asteroid by a pair of space tractors. (a) Find the cyberspace forcefulness. (b) What are the magnitude and direction of the net strength? (c) If the mass of the asteroid is 125 kg, what acceleration does information technology feel (in vector class)? (d) What are the magnitude and direction of the acceleration?

Two forces of 25 and 45 Due north act on an object. Their directions differ by [latex] 70\text{°} [/latex]. The resulting acceleration has magnitude of [latex] 10.0\,{\text{m/south}}^{2}. [/latex] What is the mass of the body?

A force of 1600 Due north acts parallel to a ramp to push a 300-kg piano into a moving van. The ramp is inclined at [latex] twenty\text{°} [/latex]. (a) What is the acceleration of the pianoforte up the ramp? (b) What is the velocity of the piano when it reaches the top if the ramp is 4.0 g long and the piano starts from rest?

Draw a complimentary-body diagram of a diver who has entered the water, moved downward, and is acted on by an upward strength due to the water which balances the weight (that is, the diver is suspended).

A free body diagram with arrow F pointing up and arrow w pointing down.

For a swimmer who has just jumped off a diving board, assume air resistance is negligible. The swimmer has a mass of lxxx.0 kg and jumps off a lath x.0 1000 higher up the water. Three seconds after inbound the h2o, her downward movement is stopped. What average upward force did the water exert on her?

(a) Find an equation to determine the magnitude of the internet strength required to stop a machine of mass yard, given that the initial speed of the auto is [latex] {v}_{0} [/latex] and the stopping altitude is x. (b) Find the magnitude of the internet force if the mass of the car is 1050 kg, the initial speed is 40.0 km/h, and the stopping distance is 25.0 g.

a. [latex] {F}_{\text{net}}=\frac{m({five}^{two}-{5}_{0}{}^{2})}{2x} [/latex]; b. 2590 N

A sailboat has a mass of [latex] one.l\,×\,{x}^{3} [/latex] kg and is acted on by a force of [latex] two.00\,×\,{x}^{iii} [/latex] North toward the east, while the current of air acts backside the sails with a force of [latex] 3.00\,×\,{10}^{iii} [/latex] North in a direction [latex] 45\text{°} [/latex] north of east. Find the magnitude and direction of the resulting acceleration.

Find the acceleration of the body of mass 10.0 kg shown beneath.

Three arrow radiate outwards from a circle labeled m. F1, equal to 10 N, points vertically down. F2, equal to 20 N, points up and right, making an angle of minus 37 degrees with the positive y axis. F3, equal to 10 N, points up and left, making an angle of 37 degrees with the positive y axis.

[latex] \brainstorm{array}{cc} {\overset{\to }{F}}_{\text{net}}=4.05\hat{i}+12.0\lid{j}\text{N}\hfill \\ {\overset{\to }{F}}_{\text{internet}}=k\overset{\to }{a}⇒\overset{\to }{a}=0.405\hat{i}+1.xx\hat{j}\,{\text{thou/southward}}^{2}\hfill \end{array} [/latex]

A body of mass two.0 kg is moving along the x-axis with a speed of three.0 g/due south at the instant represented below. (a) What is the dispatch of the torso? (b) What is the body'due south velocity 10.0 due south after? (c) What is its displacement afterward 10.0 s?

Three arrow radiate outwards from a circle labeled m. F1, equal to 50 N, points up and right, making an angle of 37 degrees with the x axis. F2, equal to 30 N, points left and down, making an angle of minus 30 degrees with the negative y axis. F3, equal to 80 N, points left.

Force [latex] {\overset{\to }{F}}_{\text{B}} [/latex] has twice the magnitude of force [latex] {\overset{\to }{F}}_{\text{A}}. [/latex] Notice the management in which the particle accelerates in this figure.

Two arrows radiate outwards from a circle labeled m. F subscript A points right. F subscript B points down and left, making an angle of 45 degrees with the horizontal.

Shown below is a body of mass 1.0 kg under the influence of the forces [latex] {\overset{\to }{F}}_{A} [/latex], [latex] {\overset{\to }{F}}_{B} [/latex], and [latex] chiliad\overset{\to }{one thousand} [/latex]. If the torso accelerates to the left at [latex] twenty\,{\text{grand/s}}^{2} [/latex], what are [latex] {\overset{\to }{F}}_{A} [/latex] and [latex] {\overset{\to }{F}}_{B} [/latex]?

Three arrows radiate outwards from a point labeled m. F subscript A points left and down, making an angle of 60 degrees with the negative x axis. F subscript B points left and up, making an angle of minus 30 degrees with the negative x axis. Vector mg points vertically down.

A force acts on a car of mass k then that the speed v of the car increases with position x as [latex] 5=thousand{ten}^{two} [/latex], where thousand is constant and all quantities are in SI units. Find the force acting on the car as a function of position.

[latex] F=2kmx [/latex]; First, accept the derivative of the velocity office to obtain [latex] a=2kx [/latex]. And so apply Newton'south second police [latex] F=ma=m(2kx)=2kmx [/latex].

A vii.0-N force parallel to an incline is applied to a 1.0-kg crate. The ramp is tilted at [latex] 20\text{°} [/latex] and is frictionless. (a) What is the acceleration of the crate? (b) If all other conditions are the aforementioned only the ramp has a friction force of ane.9 N, what is the acceleration?

Two boxes, A and B, are at rest. Box A is on level ground, while box B rests on an inclined plane tilted at bending [latex] \theta [/latex] with the horizontal. (a) Write expressions for the normal force acting on each block. (b) Compare the two forces; that is, tell which one is larger or whether they are equal in magnitude. (c) If the angle of incline is [latex] 10\text{°} [/latex], which strength is greater?

a. For box A, [latex] {North}_{\text{A}}=mg [/latex] and [latex] {Northward}_{\text{B}}=mg\,\text{cos}\,\theta [/latex]; b. [latex] {N}_{\text{A}}>{Northward}_{\text{B}} [/latex] because for [latex] \theta <90\text{°} [/latex], [latex] \text{cos}\,\theta <ane [/latex]; c. [latex] {N}_{\text{A}}>{N}_{\text{B}} [/latex] when [latex] \theta =10\text{°} [/latex]

A mass of 250.0 thousand is suspended from a spring hanging vertically. The spring stretches six.00 cm. How much will the leap stretch if the suspended mass is 530.0 g?

As shown below, two identical springs, each with the bound constant 20 N/m, support a xv.0-N weight. (a) What is the tension in leap A? (b) What is the amount of stretch of spring A from the rest position?

Figure shows two identical springs hanging side by side. Their lower ends are brought together and support a weight. Each spring makes an angle of 30 degrees with the vertical.

a. viii.66 North; b. 0.433 m

Shown below is a xxx.0-kg block resting on a frictionless ramp inclined at [latex] lx\text{°} [/latex] to the horizontal. The cake is held by a spring that is stretched v.0 cm. What is the force constant of the spring?

Figure shows a surface sloping down and left, making an angle of 60 degrees with the horizontal. An object of 30 kg hangs from a spring and rests on the slope.

In building a house, carpenters use nails from a large box. The box is suspended from a spring twice during the day to measure the usage of nails. At the beginning of the twenty-four hours, the spring stretches l cm. At the stop of the twenty-four hours, the bound stretches 30 cm. What fraction or percentage of the nails have been used?

0.40 or 40%

A force is applied to a block to move information technology up a [latex] xxx\text{°} [/latex] incline. The incline is frictionless. If [latex] F=65.0\,\text{North} [/latex] and [latex] M=five.00\,\text{kg} [/latex], what is the magnitude of the acceleration of the block?

Figure shows a surface sloping down and right, making an angle of 30 degrees with the horizontal. A box labeled M rests on it. An arrow labeled F points horizontally left towards the box. The angle formed by the arrow and the slope is 30 degrees.

Two forces are applied to a 5.0-kg object, and information technology accelerates at a rate of [latex] 2.0\,{\text{m/s}}^{two} [/latex] in the positive y-direction. If i of the forces acts in the positive x-direction with magnitude 12.0 North, find the magnitude of the other strength.

The block on the correct shown below has more mass than the block on the left ([latex] {yard}_{2}>{thousand}_{1} [/latex]). Describe free-torso diagrams for each block.

A pulley is attached to the ceiling. A rope goes over it. A block of mass m1 is attached to the left end of the rope and another block labeled m2 is attached to the right end of the rope. M2 hangs lower than m1.

Challenge Problems

If two tugboats pull on a disabled vessel, as shown here in an overhead view, the disabled vessel will exist pulled along the management indicated past the result of the exerted forces. (a) Draw a free-body diagram for the vessel. Assume no friction or drag forces affect the vessel. (b) Did y'all include all forces in the overhead view in your free-body diagram? Why or why not?

Figure shows the top view of two tugboats pulling a disabled vessel to the left. Arrow F1 is along the line connecting the vessel to the top tugboat. Arrow F2 is along the line connecting the vessel to the bottom tugboat. F1 is longer than F2. Arrow F subscript R shows the combined force. It is in between F1 and F2, pointing left and slightly up.

A ten.0-kg object is initially moving due east at xv.0 chiliad/south. Then a force acts on it for 2.00 south, afterward which information technology moves northwest, also at fifteen.0 m/southward. What are the magnitude and direction of the average force that acted on the object over the ii.00-s interval?

On June 25, 1983, shot-putter Udo Beyer of East Germany threw the seven.26-kg shot 22.22 chiliad, which at that time was a world record. (a) If the shot was released at a acme of 2.twenty thou with a projection angle of [latex] 45.0\text{°} [/latex], what was its initial velocity? (b) If while in Beyer's mitt the shot was accelerated uniformly over a distance of ane.20 k, what was the net force on it?

a. xiv.1 m/s; b. 601 North

A torso of mass m moves in a horizontal direction such that at time t its position is given by [latex] ten(t)=a{t}^{4}+b{t}^{iii}+ct, [/latex] where a, b, and c are constants. (a) What is the acceleration of the body? (b) What is the fourth dimension-dependent force interim on the body?

A trunk of mass yard has initial velocity [latex] {v}_{0} [/latex] in the positive x-direction. It is acted on past a constant force F for time t until the velocity becomes zero; the force continues to human activity on the body until its velocity becomes [latex] \text{−}{5}_{0} [/latex] in the same amount of time. Write an expression for the total distance the body travels in terms of the variables indicated.

[latex] \frac{F}{m}{t}^{2} [/latex]

The velocities of a 3.0-kg object at [latex] t=half-dozen.0\,\text{southward} [/latex] and [latex] t=8.0\,\text{s} [/latex] are [latex] (iii.0\hat{i}-6.0\chapeau{j}+iv.0\lid{m})\,\text{g/s} [/latex] and [latex] (-two.0\hat{i}+4.0\chapeau{k})\,\text{m/southward} [/latex], respectively. If the object is moving at constant acceleration, what is the force acting on it?

A 120-kg astronaut is riding in a rocket sled that is sliding forth an inclined plane. The sled has a horizontal component of acceleration of [latex] 5.0\,\text{g}\text{/}{\text{s}}^{two} [/latex] and a downwardly component of [latex] 3.8\,\text{chiliad}\text{/}{\text{s}}^{2} [/latex]. Calculate the magnitude of the strength on the rider past the sled. (Hint: Remember that gravitational acceleration must exist considered.)

Two forces are acting on a 5.0-kg object that moves with acceleration [latex] ii.0\,{\text{grand/s}}^{2} [/latex] in the positive y-management. If one of the forces acts in the positive x-direction and has magnitude of 12 N, what is the magnitude of the other force?

Suppose that you are viewing a soccer game from a helicopter in a higher place the playing field. 2 soccer players simultaneously kicking a stationary soccer ball on the flat field; the soccer ball has mass 0.420 kg. The beginning player kicks with force 162 N at [latex] 9.0\text{°} [/latex] n of west. At the same instant, the 2nd player kicks with force 215 N at [latex] 15\text{°} [/latex] due east of s. Discover the acceleration of the ball in [latex] \hat{i} [/latex] and [latex] \chapeau{j} [/latex] form.

[latex] [/latex][latex] \overset{\to }{a}=-248\hat{i}-433\lid{j}\text{thousand}\text{/}{\text{south}}^{2} [/latex]

A x.0-kg mass hangs from a spring that has the spring constant 535 Due north/m. Discover the position of the end of the spring away from its residual position. (Use [latex] yard=9.80\,{\text{yard/s}}^{two} [/latex].)

A 0.0502-kg pair of fuzzy dice is fastened to the rearview mirror of a car past a brusk cord. The motorcar accelerates at abiding rate, and the dice hang at an angle of [latex] three.twenty\text{°} [/latex] from the vertical considering of the car's acceleration. What is the magnitude of the acceleration of the car?

[latex] 0.548\,{\text{m/s}}^{ii} [/latex]

At a circus, a donkey pulls on a sled conveying a small clown with a forcefulness given by [latex] 2.48\hat{i}+4.33\hat{j}\,\text{Northward} [/latex]. A horse pulls on the same sled, aiding the hapless ass, with a force of [latex] 6.56\hat{i}+5.33\hat{j}\,\text{N} [/latex]. The mass of the sled is 575 kg. Using [latex] \hat{i} [/latex] and [latex] \hat{j} [/latex] form for the answer to each problem, find (a) the cyberspace forcefulness on the sled when the two animals act together, (b) the dispatch of the sled, and (c) the velocity afterward 6.fifty s.

Hanging from the ceiling over a baby bed, well out of infant's reach, is a string with plastic shapes, as shown hither. The cord is taut (there is no slack), as shown by the directly segments. Each plastic shape has the same mass m, and they are equally spaced past a altitude d, every bit shown. The angles labeled [latex] \theta [/latex] describe the angle formed by the end of the string and the ceiling at each end. The center length of sting is horizontal. The remaining ii segments each form an angle with the horizontal, labeled [latex] \varphi [/latex]. Let [latex] {T}_{one} [/latex] exist the tension in the leftmost section of the string, [latex] {T}_{2} [/latex] be the tension in the section adjacent to it, and [latex] {T}_{iii} [/latex] be the tension in the horizontal segment. (a) Find an equation for the tension in each section of the string in terms of the variables 1000, thousand, and [latex] \theta [/latex]. (b) Observe the angle [latex] \varphi [/latex] in terms of the angle [latex] \theta [/latex]. (c) If [latex] \theta =5.10\text{°} [/latex], what is the value of [latex] \varphi [/latex]? (d) Find the altitude 10 between the endpoints in terms of d and [latex] \theta [/latex].

Figure shows four shapes hanging on a string that is attached to the ceiling at both ends. The shapes divide the string in five equal segments, each having length d. The middle segment is horizontal. The distance between the two ends of the string is x. The angles between the ceiling and the segments closest to the ceiling are both labeled theta. The angles formed by the first segments from the ceiling with their adjoining segments are both labeled phi.

a. [latex] {T}_{1}=\frac{2mg}{\text{sin}\,\theta } [/latex], [latex] {T}_{2}=\frac{mg}{\text{sin}(\text{arctan}(\frac{i}{2}\text{tan}\,\theta ))} [/latex], [latex] {T}_{3}=\frac{2mg}{\text{tan}\,\theta }; [/latex] b. [latex] \varphi =\text{arctan}(\frac{1}{ii}\text{tan}\,\theta ) [/latex]; c. [latex] 2.56\text{°} [/latex]; (d) [latex] x=d(2\,\text{cos}\,\theta +2\,\text{cos}(\text{arctan}(\frac{1}{two}\text{tan}\,\theta ))+1) [/latex]

A bullet shot from a rifle has mass of 10.0 one thousand and travels to the correct at 350 one thousand/s. It strikes a target, a big purse of sand, penetrating information technology a distance of 34.0 cm. Detect the magnitude and direction of the retarding forcefulness that slows and stops the bullet.

An object is acted on by three simultaneous forces: [latex] {\overset{\to }{F}}_{one}=(-3.00\hat{i}+2.00\chapeau{j})\,\text{Due north} [/latex], [latex] {\overset{\to }{F}}_{ii}=(6.00\hat{i}-4.00\lid{j})\,\text{North} [/latex], and [latex] {\overset{\to }{F}}_{3}=(2.00\hat{i}+5.00\lid{j})\,\text{N} [/latex]. The object experiences acceleration of [latex] 4.23\,{\text{m/south}}^{2} [/latex]. (a) Find the acceleration vector in terms of one thousand. (b) Find the mass of the object. (c) If the object begins from rest, notice its speed after 5.00 due south. (d) Find the components of the velocity of the object subsequently 5.00 s.

a. [latex] \overset{\to }{a}=(\frac{v.00}{m}\chapeau{i}+\frac{3.00}{1000}\lid{j})\,\text{thou}\text{/}{\text{s}}^{2}; [/latex] b. 1.38 kg; c. 21.two m/south; d. [latex] \overset{\to }{five}=(xviii.1\hat{i}+10.9\hat{j})\,\text{1000}\text{/}{\text{s}}^{ii} [/latex]

In a particle accelerator, a proton has mass [latex] ane.67\,×\,{10}^{-27}\,\text{kg} [/latex] and an initial speed of [latex] 2.00\,×\,{10}^{5}\,\text{one thousand}\text{/}\text{s.} [/latex] It moves in a straight line, and its speed increases to [latex] nine.00\,×\,{ten}^{5}\,\text{1000}\text{/}\text{due south} [/latex] in a distance of 10.0 cm. Assume that the dispatch is constant. Find the magnitude of the force exerted on the proton.

A drone is existence directed across a frictionless ice-covered lake. The mass of the drone is 1.50 kg, and its velocity is [latex] three.00\hat{i}\text{m}\text{/}\text{s} [/latex]. Later 10.0 s, the velocity is [latex] 9.00\hat{i}+4.00\chapeau{j}\text{grand}\text{/}\text{s} [/latex]. If a abiding forcefulness in the horizontal direction is causing this change in motility, find (a) the components of the force and (b) the magnitude of the force.

a. [latex] 0.900\hat{i}+0.600\lid{j}\,\text{Due north} [/latex]; b. ane.08 N

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Source: https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/5-7-drawing-free-body-diagrams/

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