Assume That I = 14 a (Figure 1) You May Want to Review (Pages 803 - 806)

5.1 Forces

19 .

Two ropes are fastened to a tree, and forces of ${\overrightarrow{F}}_{\mathrm{ane}}=\mathrm{two.0}\widehat{i}+\mathrm{iv.0}\widehat{j}\text{N}$ and ${\overrightarrow{F}}_{\mathrm{ii}}=\mathrm{three.0}\widehat{i}+\mathrm{six.0}\widehat{j}\text{North}$ are applied. The forces are coplanar (in the same plane). (a) What is the resultant (internet forcefulness) of these ii force vectors? (b) Find the magnitude and direction of this net force.

20 .

A telephone pole has 3 cables pulling equally shown from above, with ${\overrightarrow{F}}_1=\left(300.0\widehat{i}+500.0\widehat{j}\right)$ , ${\overrightarrow{F}}_2=\mathrm{-200.0}\widehat{i}$ , and ${\overrightarrow{F}}_3=\mathrm{-800.0}\widehat{j}$ . (a) Find the net force on the telephone pole in component grade. (b) Find the magnitude and management of this net force.

21 .

Ii teenagers are pulling on ropes fastened to a tree. The angle between the ropes is $30.0\text{°}$ . David pulls with a force of 400.0 N and Stephanie pulls with a force of 300.0 N. (a) Find the component grade of the net force. (b) Observe the magnitude of the resultant (internet) force on the tree and the bending information technology makes with David's rope.

five.2 Newton's First Law

22 .

Two forces of ${\overrightarrow{F}}_1=\frac{75.0}{\sqrt{\mathrm{two}}}\left(\widehat{i}-\widehat{j}\right)\text{N}$ and ${\overrightarrow{F}}_2=\frac{150.0}{\sqrt{\mathrm{ii}}}\left(\widehat{i}-\widehat{j}\right)\text{N}$ deed on an object. Detect the third force ${\overrightarrow{F}}_3$ that is needed to residue the offset 2 forces.

23 .

While sliding a burrow beyond a floor, Andrea and Jennifer exert forces ${\overrightarrow{F}}_{\text{A}}$ and ${\overrightarrow{F}}_{\text{J}}$ on the couch. Andrea's force is due due north with a magnitude of 130.0 N and Jennifer's force is $32\text{°}$ due east of north with a magnitude of 180.0 N. (a) Notice the net strength in component form. (b) Find the magnitude and direction of the cyberspace force. (c) If Andrea and Jennifer'south housemates, David and Stephanie, disagree with the motion and want to prevent its relocation, with what combined force ${\overrightarrow{F}}_{\text{DS}}$ should they push so that the couch does not motility?

5.3 Newton's 2nd Constabulary

24 .

Andrea, a 63.0-kg sprinter, starts a race with an acceleration of $4.200{\text{m/due south}}^2$ . What is the cyberspace external force on her?

25 .

If the sprinter from the previous trouble accelerates at that rate for xx.00 m and then maintains that velocity for the remainder of a 100.00-m dash, what volition her time be for the race?

26 .

A cleaner pushes a four.l-kg laundry cart in such a fashion that the net external forcefulness on it is 60.0 North. Calculate the magnitude of his cart's acceleration.

27 .

Astronauts in orbit are apparently weightless. This means that a clever method of measuring the mass of astronauts is needed to monitor their mass gains or losses, and adjust their diet. 1 way to practise this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 N is exerted, and an astronaut's acceleration is measured to be $0.893{\text{m/south}}^{\mathrm{two}}$ . (a) Calculate her mass. (b) Past exerting a forcefulness on the astronaut, the vehicle in which she orbits experiences an equal and opposite force. Use this cognition to find an equation for the acceleration of the system (astronaut and spaceship) that would be measured past a nearby observer. (c) Discuss how this would affect the measurement of the astronaut's acceleration. Advise a method past which recoil of the vehicle is avoided.

28 .

In Effigy five.12, the internet external force on the 24-kg mower is given every bit 51 Due north. If the strength of friction opposing the move is 24 N, what strength F (in newtons) is the person exerting on the mower? Suppose the mower is moving at one.five m/southward when the force F is removed. How far will the mower go before stopping?

29 .

The rocket sled shown beneath accelerates opposite to the motion at a rate of $196{\text{1000/s}}^{\mathrm{two}}$ . What force is necessary to produce this acceleration contrary to the motion? Assume that the rockets are off. The mass of the system is $2.10\times {10}^3$ kg.

xxx .

If the rocket sled shown in the previous problem starts with only one rocket called-for, what is the magnitude of this acceleration? Assume that the mass of the system is $2.10\times {10}^3$ kg, the thrust T is $\mathrm{ii.40}\times {10}^{\mathrm{four}}\text{N},$ and the force of friction opposing the movement is 650.0 N. (b) Why is the acceleration non one-fourth of what it is with all rockets called-for?

31 .

What is the dispatch opposite to the motion of the rocket sled if information technology comes to remainder in i.10 due south from a speed of 1000.0 km/h? (Such acceleration opposite to the motility acquired one test discipline to black out and have temporary blindness.)

32 .

Suppose 2 children button horizontally, just in exactly opposite directions, on a third child in a wagon. The first child exerts a strength of 75.0 Due north, the 2nd exerts a force of 90.0 N, friction is 12.0 N, and the mass of the third child plus wagon is 23.0 kg. (a) What is the organisation of interest if the acceleration of the kid in the wagon is to be calculated? (Run across the free-body diagram.) (b) Summate the acceleration. (c) What would the acceleration exist if friction were 15.0 N?

33 .

A powerful motorcycle tin produce an acceleration of $\mathrm{three.50}{\text{yard/s}}^{\mathrm{ii}}$ while traveling at 90.0 km/h. At that speed, the forces resisting motion, including friction and air resistance, full 400.0 N. (Air resistance is analogous to air friction. Information technology always opposes the motion of an object.) What is the magnitude of the forcefulness that motorcycle exerts backward on the footing to produce its dispatch if the mass of the motorbike with rider is 245 kg?

34 .

A automobile with a mass of k.0 kg accelerates from 0 to 90.0 km/h in 10.0 s. (a) What is its acceleration? (b) What is the net force on the machine?

35 .

The driver in the previous trouble applies the brakes when the machine is moving at 90.0 km/h, and the auto comes to rest after traveling xl.0 k. What is the cyberspace force on the machine during its acceleration opposite to the motion?

36 .

An 80.0-kg passenger in an SUV traveling at $1.00\times {\mathrm{ten}}^2$ km/h is wearing a seat belt. The driver slams on the brakes and the SUV stops in 45.0 g. Find the force of the seat belt on the rider.

37 .

A particle of mass 2.0 kg is acted on past a unmarried force ${\overrightarrow{F}}_{\mathrm{one}}=18\widehat{i}\text{N}.$ (a) What is the particle'southward acceleration? (b) If the particle starts at remainder, how far does it travel in the first 5.0 s?

38 .

Suppose that the particle of the previous trouble also experiences forces ${\overrightarrow{F}}_{\mathrm{ii}}=\mathrm{-15}\widehat{i}\text{Northward}$ and ${\overrightarrow{F}}_{\mathrm{three}}=\mathrm{half\; dozen.0}\widehat{j}\text{Due north}.$ What is its acceleration in this case?

39 .

Observe the dispatch of the body of mass 5.0 kg shown below.

40 .

In the following effigy, the horizontal surface on which this block slides is frictionless. If the ii forces interim on it each have magnitude $F=\mathrm{xxx.0}\text{N}$ and $M=\mathrm{x.0}\text{kg}$ , what is the magnitude of the resulting dispatch of the cake?

5.iv Mass and Weight

41 .

The weight of an astronaut plus his infinite suit on the Moon is only 250 N. (a) How much does the suited astronaut counterbalance on Earth? (b) What is the mass on the Moon? On Earth?

42 .

Suppose the mass of a fully loaded module in which astronauts take off from the Moon is $\mathrm{ane.00}\times {10}^{\mathrm{four}}$ kg. The thrust of its engines is $3.00\times {10}^4$ Northward. (a) Calculate the module's magnitude of acceleration in a vertical takeoff from the Moon. (b) Could information technology lift off from Earth? If non, why not? If it could, summate the magnitude of its dispatch.

43 .

A rocket sled accelerates at a rate of ${49.0\text{g/s}}^2$ . Its passenger has a mass of 75.0 kg. (a) Calculate the horizontal component of the strength the seat exerts against his body. Compare this with his weight using a ratio. (b) Calculate the management and magnitude of the full force the seat exerts against his torso.

44 .

Repeat the previous problem for a situation in which the rocket sled accelerates reverse to the motion at a rate of ${201\text{g/s}}^2$ . In this problem, the forces are exerted by the seat and the seat belt.

45 .

A body of mass 2.00 kg is pushed direct upwards by a 25.0 Due north vertical force. What is its dispatch?

46 .

A automobile weighing 12,500 N starts from rest and accelerates to 83.0 km/h in v.00 south. The friction strength is 1350 N. Notice the practical forcefulness produced past the engine.

47 .

A torso with a mass of ten.0 kg is causeless to be in Earth'southward gravitational field with $\mathrm{1000}=9.80{\text{thousand/south}}^2$ . What is the net force on the body if there are no other external forces interim on the object?

48 .

A fireman has mass m; he hears the burn alarm and slides down the pole with acceleration a (which is less than g in magnitude). (a) Write an equation giving the vertical strength he must use to the pole. (b) If his mass is xc.0 kg and he accelerates at $\mathrm{five.00}{\text{m/s}}^2,$ what is the magnitude of his applied force?

49 .

A baseball catcher is performing a stunt for a television commercial. He will catch a baseball (mass 145 1000) dropped from a height of threescore.0 one thousand in a higher place his glove. His glove stops the ball in 0.0100 s. What is the forcefulness exerted by his glove on the ball?

50 .

When the Moon is direct overhead at dusk, the force past Earth on the Moon, $F_{\text{EM}}$ , is essentially at $\mathrm{ninety}\text{°}$ to the forcefulness past the Sun on the Moon, $F_{\text{SM}}$ , as shown below. Given that $F_{\text{EM}}=\mathrm{i.98}\times {10}^{20}\text{N}$ and $F_{\text{SM}}=\mathrm{four.36}\times {10}^{\mathrm{twenty}}\text{North},$ all other forces on the Moon are negligible, and the mass of the Moon is $7.35\times {10}^{22}\text{kg},$ make up one's mind the magnitude of the Moon'south dispatch.

5.5 Newton's 3rd Law

51 .

(a) What net external forcefulness is exerted on a 1100.0-kg artillery shell fired from a battleship if the crush is accelerated at $2.40\times {10}^4{\text{m/south}}^{\mathrm{two}}?$ (b) What is the magnitude of the force exerted on the transport by the artillery shell, and why?

52 .

A dauntless but inadequate rugby histrion is beingness pushed backward past an opposing player who is exerting a strength of 800.0 N on him. The mass of the losing role player plus equipment is 90.0 kg, and he is accelerating astern at $1.20{\text{m/southward}}^{\mathrm{two}}$ . (a) What is the force of friction between the losing player'due south anxiety and the grass? (b) What force does the winning thespian exert on the ground to move forward if his mass plus equipment is 110.0 kg?

53 .

A history book is lying on top of a physics book on a desk, as shown below; a free-body diagram is also shown. The history and physics books weigh fourteen N and 18 Northward, respectively. Identify each force on each book with a double subscript annotation (for instance, the contact forcefulness of the history book pressing confronting physics book can be described as ${\overrightarrow{F}}_{\text{HP}}$ ), and determine the value of each of these forces, explaining the procedure used.

54 .

A truck collides with a car, and during the standoff, the internet force on each vehicle is essentially the force exerted by the other. Suppose the mass of the machine is 550 kg, the mass of the truck is 2200 kg, and the magnitude of the truck's dispatch is $10{\text{g/s}}^2$ . Find the magnitude of the machine's dispatch.

five.half-dozen Mutual Forces

55 .

A leg is suspended in a traction system, as shown beneath. (a) Which pulley in the figure is used to summate the force exerted on the human foot? (b) What is the tension in the rope? Here $\overrightarrow{T}$ is the tension, ${\overrightarrow{w}}_{\text{leg}}$ is the weight of the leg, and $\overrightarrow{\mathrm{west}}$ is the weight of the load that provides the tension.

56 .

Suppose the shinbone in the preceding paradigm was a femur in a traction setup for a broken bone, with pulleys and rope available. How might we be able to increment the force along the femur using the aforementioned weight?

57 .

Two teams of nine members each engage in a tug-of-war, pulling in contrary directions on a horizontal rope. Each of the first squad'southward members has an average mass of 68 kg and exerts an average forcefulness of 1350 N horizontally on the footing equally they pull on the rope. Each of the second team'southward members has an average mass of 73 kg and exerts an average force of 1365 N horizontally on the basis as they pull on the rope in the reverse management. (a) What is the magnitude of the acceleration of the ii teams, and which team wins? (b) What is the tension in the section of rope between the teams?

58 .

What strength does a trampoline have to apply to Jennifer, a 45.0-kg gymnast, to accelerate her straight up at $\mathrm{vii.50}{\text{m/s}}^{\mathrm{ii}}$ ? The answer is independent of the velocity of the gymnast—she tin can be moving up or downward or can be instantly stationary.

59 .

(a) Calculate the tension in a vertical strand of web if a spider of mass $2.00\times {\mathrm{ten}}^{\mathrm{-5}}\text{kg}$ hangs motionless on information technology. (b) Calculate the tension in a horizontal strand of spider web if the same spider sits motionless in the middle of it much like the tightrope walker in Figure 5.26. The strand sags at an angle of $12\text{°}$ below the horizontal. Compare this with the tension in the vertical strand (notice their ratio).

60 .

Suppose Kevin, a 60.0-kg gymnast, climbs a rope. (a) What is the tension in the rope if he climbs at a constant speed? (b) What is the tension in the rope if he accelerates upward at a rate of $1.50{\text{m/s}}^2$ ?

61 .

Show that, as explained in the text, a force $F_{\perp }$ exerted on a flexible medium at its center and perpendicular to its length (such equally on the tightrope wire in Figure five.26) gives rise to a tension of magnitude $T=F_{\perp }\text{/}2\text{sin}\left(\theta \right)$ .

62 .

Consider Figure 5.28. The driver attempts to get the car out of the mud past exerting a perpendicular strength of 610.0 N, and the distance she pushes in the centre of the rope is ane.00 yard while she stands vi.00 g away from the car on the left and vi.00 one thousand away from the tree on the right. What is the tension T in the rope, and how do you lot find the answer?

63 .

A bird has a mass of 26 1000 and perches in the centre of a stretched telephone line. (a) Testify that the tension in the line tin exist calculated using the equation $T=\frac{mg}{\mathrm{two}\text{sin}\theta }$ . Determine the tension when (b) $\theta =5\text{°}$ and (c) $\theta =\mathrm{0.v}\text{°}$ . Assume that each half of the line is straight.

64 .

One end of a 30-thousand rope is tied to a tree; the other finish is tied to a car stuck in the mud. The motorist pulls sideways on the midpoint of the rope, displacing it a distance of 2 m. If he exerts a forcefulness of 80 North under these conditions, decide the force exerted on the car.

65 .

Consider the baby being weighed in the following figure. (a) What is the mass of the infant and basket if a scale reading of 55 N is observed? (b) What is tension $T_{\mathrm{one}}$ in the cord attaching the baby to the scale? (c) What is tension $T_2$ in the cord attaching the scale to the ceiling, if the calibration has a mass of 0.500 kg? (d) Sketch the situation, indicating the organization of interest used to solve each part. The masses of the cords are negligible.

66 .

What force must be applied to a 100.0-kg crate on a frictionless plane inclined at $30\text{°}$ to cause an dispatch of ${2.0\text{k/s}}^2$ upwards the plane?

67 .

A 2.0-kg block is on a perfectly smooth ramp that makes an angle of $\mathrm{thirty}\text{°}$ with the horizontal. (a) What is the block's acceleration downwardly the ramp and the forcefulness of the ramp on the block? (b) What force practical upward along and parallel to the ramp would allow the cake to movement with constant velocity?

five.vii Drawing Free-Trunk Diagrams

68 .

A brawl of mass grand hangs at residual, suspended by a string. (a) Sketch all forces. (b) Draw the free-torso diagram for the ball.

69 .

A car moves along a horizontal route. Draw a gratis-body diagram; exist sure to include the friction of the road that opposes the forwards move of the car.

70 .

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

(credit: modification of piece of work by "Greenwich Photography"/Flickr)

71 .

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

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Source: https://openstax.org/books/university-physics-volume-1/pages/5-problems

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