Assignment - Forces

Reading:  Chapter 4




The student will be able to:



State Newton’s 1st and 2nd Laws of Motion and apply these laws to physical situations in order to determine what forces act on an object and to explain the object’s resulting behavior.

1 – 5


Recognize and state the proper SI unit of force and give its equivalence in fundamental units and use the relation Fnet = ma to solve problems.

6 – 10


Recognize the difference between weight and mass and convert from one to the other.

11 – 18


State and utilize Newton’s 3rd Law to solve related problems.

19 – 21


Understand and utilize the concept of the normal force to solve related problems.

22 – 25


Understand and utilize the relation between friction force, normal force, and coefficient of friction for both cases:  static and kinetic.

26 – 32


Resolve forces into components using trigonometry and use the results to solve related force problems.

33 – 37


Apply the concept of force components to objects on an incline and solve related problems.

38 – 42


Homework Problems


1.      Using Newton’s Laws explain why you must push harder on the pedals of a single-speed bicycle to start it moving than to keep it moving with a constant velocity.

2.      Suppose you have a nearly empty jar of salsa that you want to pour into a bowl.  Of course you will turn the jar upside down – but sometimes this is not enough to get the salsa out of the jar.  Usually you will not only turn the jar over but also shake it up and down.  Use Newton’s Laws to explain why shaking helps the salsa come out of the jar.

3.      The Pioneer 10 spacecraft has left our Solar System and is traveling at a speed of 29,000 mph (and has been doing so for years).  Explain why this object is moving so fast although it ran out of fuel long ago.

4.      A person in a car that is struck from behind can receive a serious neck injury called whiplash due to his head “whipping backward”.  (a) Use Newton’s Laws to explain what happens to the person’s head.  (b) Use Newton’s Laws to explain how a headrest helps to reduce whiplash injuries.

5.      When the space shuttle is launched from Earth, a constant force is applied and the shuttle accelerates upward.  As the flight progresses, its rate of acceleration increases.  Explain using Newton’s Laws.

6.      A net force of 150 N causes a certain person to accelerate 1.20 m/s2.  Determine the person’s mass.

7.      A certain car (Mazda Miata) has a mass of 1080 kg and can go from zero to 26.8 m/s (0 to 60 mph) in 7.9 seconds.  What magnitude net force must act on the car to cause this?

8.      The Deep Space 1 spacecraft’s ion engine produced an average thrust of 37 mN and was fired for a total of 16000 hours.  The mass of the spacecraft was 450 kg.  (a) Assuming this thrust was the only force acting on it what was the spacecraft’s rate of acceleration?  (b) By how much was its velocity changed over this time period?

9.      Two forces act on a falling skydiver with mass 100 kg:  a downward gravity force and an upward air resistance (friction) force.  Suppose the net force on the skydiver is 670 N, 270.0° – this means the gravity force is 670 N greater than the friction force.  (a) Determine the resulting acceleration.  Just after the parachute opens, the acceleration is 5.0 m/s2, 90.0°.  (b) Determine the net force at this point.  (c) Which force is larger now and by how much?

10.  Suppose you hook a 1.5 kg fish while using line that is rated at 38 N (it can only sustain that much force before breaking – about “9-lb test”).  If the fish fights back with 40 N of force, what is the minimum acceleration rate you must play out the line in order to keep it from breaking?

11.  (a) Compare the amount of force needed to lift a 10 kg rock on the Earth and on the Moon – which is greater and why?.  (b) Now compare the amount of force needed to throw the same rock horizontally at the same speed in the two locations.  Explain.

12.  A 95.0 kg (209 lb) boxer has matches in the Canal Zone (g = 9.782 m/s2) and in the Arctic Circle (g = 9.832 m/s2).  (a) What is his mass in the Canal Zone?  (b) What is his weight in the Canal Zone?  (c) What is his mass in the Arctic Circle?  (c) What is his weight in the Arctic Circle?  (e)Based on this, should a scale or a balance be used for the “weigh-in”?

13.  Suppose a certain motorcycle weighs 2450 N.  What is its mass in kilograms?

14.  A 4500 kg helicopter accelerates upward at 2.0 m/s2.  What lift force is exerted on the propellers by the air?

15.  Safety engineers estimate that an elevator “car” can hold 20 persons of 75 kg average mass.  The car itself has a mass of 500 kg.  Tensile strength tests show that the cable supporting the car can tolerate a maximum force of 29.6 kN.  What is the greatest acceleration that the elevator’s motor can produce in the fully loaded car without breaking the cable?

16.  An elevator car that weighs 3.0 kN is accelerated upward at 1.3 m/s2.  What force does the cable exert to give it this acceleration?

17.  A rocket with a mass of 23.0 Mg is sitting vertically on a launch pad.  The rocket’s engine fires to produce a thrust of 680 kN.  (a) What is the net force acting on the rocket just as it leaves the ground?  (b) What is the acceleration of the rocket?

18.  A person throws a ball with mass 175 g.  If the person’s hand exerts a force of 5.00 N, 50.0°, what will be the resulting acceleration of the ball?  (You must include the effect of gravity.)

19.  Mules are smart but stubborn.  Once upon a time a particularly smart and particularly stubborn mule refused to pull its owner’s cart and gave the following argument:  “I refuse to pull the cart because it is impossible to do so according to Newton’s laws of motion.  According to the 2nd Law it is necessary to have a net force in order for the cart to accelerate.  According to the 3rd Law no matter how hard I pull the cart forward, the cart will pull an equal amount backward and therefore the net force will be zero and the cart will not move.  Even if I could pull a million Newtons forward, the cart would pull a million Newtons backward and so I refuse to even try!”  What is the flaw in the mule’s argument?

20.  When you drop a 0.40 kg apple, Earth exerts a force on it that accelerates it toward the Earth’s surface.  Assuming Newton’s Laws are true (and they are!) the Earth must also accelerate toward the apple.  (a) Given its mass is 5.974 x 1024 kg, determine the rate at which the Earth accelerates upward toward the falling apple.  (b) Determine how far the Earth moves up during the time that the apple moves down 1.0 m.

21.  A 115 kg astronaut on a space walk pushes against her space capsule that has mass 2250 kg.  The astronaut accelerates 1.50 m/s2, 0°.  (a) Find the force exerted on the astronaut.  (b) Find the force exerted on the capsule.  (c) Find the acceleration of the capsule.

22.  Suppose a 200 g ball is in contact with the floor.  (a) Determine the normal force the floor exerts on the ball when it is at rest.  (b) Determine the normal force the floor exerts on the ball when it is bouncing and accelerating upward 100 m/s2.  (c) Determine the force that the ball exerts on the floor as it is bouncing with acceleration 100 m/s2, 90.0°.

23.  The maximum force a grocery sack can withstand and not rip is 250 N.  If 20 kg of groceries are lifted from the floor to the table with an acceleration of 5.0 m/s2, will the sack hold?  Assume the person’s hand is not underneath the sack.  Hint:  draw a free body diagram of the sack’s contents (treat as a single object).

24.  A person stands on a bathroom scale in an elevator at rest on the ground floor of a building.  The scale then reads 836 N.  As the elevator begins to move upward, the scale reading briefly increases to 935 N but then returns to 836 N.  As the elevator reaches the 20th floor, the scale reading briefly drops to 782 N and then once again returns to 836 N once it has stopped.  (a) Determine the elevator’s acceleration as its speed increases.  (b) Determine the elevator’s acceleration as its speed decreases.  (c) Explain why the scale reads 836 N for most of the elevator’s trip.

25.   A person lifts a stack of two boxes by exerting a force of 60.0N upward on the bottom of the lower box.  Both boxes accelerate upward at the same rate. The upper box is 2.00 kg and the lower box is 3.00 kg.  (a) Draw a free-body diagram of the stack of boxes (treat as one object) and solve for the acceleration.  (b) Draw a free-body diagram of the upper box and solve for the normal force pushing up on it.  (c) Draw a free-body diagram of the lower box and solve for the normal force pushing down on it.  (d) Explain how these results are consistent with Newton’s 3rd Law of motion.

26.  A sled of mass 50 kg is pulled horizontally over flat ground.  The static friction coefficient is 0.30, and the sliding friction coefficient is 0.10.  (a) What does the sled weigh?  (b) What minimum amount of force must be applied to the sled in order to start it moving?  (c) What amount of applied force will keep it moving at a constant velocity of 3.0 m/s?  (d) What amount of applied force will accelerate the sled at 3.0 m/s2?

27.  A force of 40 N, 180° accelerates a 5.0 kg block at 6.0 m/s2, 180° along a horizontal surface.  (a) Determine the force of friction acting on the block.  (b) Determine the coefficient of friction.

28.  A 20 kg wagon is rolling to the right across a floor.  A person attempts to catch and stop the wagon and applies a force of 70 N, 180.0° on it.  If the coefficient of friction is 0.18, calculate the deceleration rate of the wagon as it is caught.

29.  Two brothers are goofing around on the surface of a frozen lake where m=0.050.  The older brother weighs 825 N and the younger weighs 765 N.  The older brother shoves the younger with a force of 85.0 N, 0.0°  (a) Find the acceleration of the younger brother.  (b) Find the acceleration of the older brother.

30.  A truck accelerates from rest toward 0.0°.  In the bed of the truck is a 15 kg crate for which mstatic = 0.20 and msliding = 0.15.  (a) What is the maximum acceleration rate at which the crate will not slide across the bed?  (b) If the truck exceeds this, what will be the acceleration of the crate?

31.  A truck with mass 2000 kg tows a boat and trailer of total mass 500 kg.  The rolling coefficient of friction for the truck is 0.080 and for the trailer is 0.050.  The force of the truck’s drive wheels pushing backward on the pavement is 3.0 kN.  (a) Determine the acceleration rate of the truck and trailer moving forward together.  (b) Determine the amount of force the truck’s hitch exerts forward on the trailer.

32.  A 275 kg mule pushes backward with its feet 1.50 kN, 180.0° on the ground as it pulls a cart forward.  The mule and the cart both accelerate forward 0.500 m/s2, 0.0°. (a) What force does the mule exert on the cart?  (b) Assuming the coefficient of friction for the cart is 0.25, what is its mass?

33.  A 40 kg crate is pulled across the ice with a rope.  A force of 100 N, 30° is applied by the rope.  Assume friction is negligible.  (a) Determine the acceleration of the crate.  (b) Determine the normal force that the crate exerts on the ice.

34.  A suitcase with mass 18 kg is pulled at a constant speed by a handle that makes an angle q with the horizontal.  The frictional force on the suitcase is 27 N and the force applied on the handle is 43 N. (a) Determine the value of the angle, q.  (b) Determine the normal force exerted on the suitcase.

35.  A traffic signal weighs 150 N and hangs above an intersection.  It is supported equally by wires on either side that form an angle of 120.0° with each other.  (a) What is the tension in each of these wires?  (b) If the angle between the wires is increased to 140.0°, what is the new tension?  (c) As the wires get closer to horizontal what happens to the tension?

36.  Joe hangs a sign weighing 750 N with two cables.  Cable A is directed toward 120.0°.  Cable B is directed toward 0.0°.  Nothing but these two cables supports the sign.  Calculate the tension in cable B. 

37.  A person exerts a force of 175 N, 210.0° on a 20.0 kg crate which slides to the left across a level floor where m = 0.400.  (a) Find the normal force on the crate.  (b) Find the force of friction on the crate.  (c) Find the acceleration of the crate.

38.  You slide a 325 N trunk up a 20.0° inclined plane with a constant velocity by exerting a force of 211 N parallel to the inclined plane.  (a) Determine the component of the trunk’s weight parallel to the plane.  (b) What would be the sum of your applied force, friction, and the parallel component of the trunk’s weight and why?  (c) Determine the friction acting on the trunk.  (d) Determine the coefficient of friction.

39.  A 475 gram box is given a push and it then slides up and back down a ramp with a 35.0° incline.  The coefficient of friction is 0.30.  (a) Determine the rate of deceleration as the box slides up the ramp.  (b) Determine the rate of acceleration as the box slides back down the ramp.  (c)  Determine the amount of applied force necessary to push the box up the ramp at a steady speed.

40.  A snow skier of mass 85.0 kg slides with constant velocity down a slope that makes an angle of 10.0° with the horizontal.  (a) What is the coefficient of sliding friction?  (b) If the slope increases to 15.0° what will be the skier’s rate of acceleration?

41.  Choose and solve one of the following problems from your book, pp. 104 – 111: 
19, 20, 34, 36, 46, 57, 60, 64, 67, 77

42.  Choose and solve another one of the following problems from your book, pp. 104 – 111: 
19, 20, 34, 36, 46, 57, 60, 64, 67, 77

Answers to Selected Homework Problems:







6. 125 kg

7. 3700 N

8. a. 8.2 ´ 10-5 m/s2

    b. 4700 m/s

9. a. 6.70 m/s2, 270.0°

    b. 500 N, 90.0°


10. 1.3 m/s2


12. a.

      b. 929 N


      d. 934 N


13. 250 kg

14. 53 kN, 90°

15. 5.0 m/s2, 90°

16. 3400 N, 90°

17. a. 455 kN, 90.0°

      b. 19.8 m/s2, 90.0°

18. 22.0 m/s2, 33.4°


20. a. 6.6 ´ 10-25 m/s2

      b. 6.7 ´ 10-26 m
          (~ 1/10-billion the width of a single proton!)

21. a. 173 N, 0.0°

      b. 173 N, 180.0°

      c. 76.6 mm/s2, 180.0°

22. a. 1.96 N, 90.0°

      b. 22.0 N, 90.0°


23. No, the sack will rip – would need to

      withstand 300 N or not exceed 2.7 m/s2

24. a. 1.2 m/s2, 90°

      b. 0.63 m/s2, 270°


25. a. 2.2 m/s2, 90.0°

      b. 24.0 N, 90.0°

      c. 24.0 N, 270.0°


26. a. 490 N

      b. 150 N

      c. 49 N

      d. 200 N

27. a. 10 N

      b. 0.20

28. 5.3 m/s2

29. a. 0.599 m/s2, 0.0°

      b. 0.520 m/s2, 180.0°

30. a. 2.0 m/s2

      b. 1.5 m/s2

31. a. 0.47 m/s2

      b. 480 N

32. a. 1360 N, 0.0°

      b. 462 kg

33. a. 2.2 m/s2, 0.0°

      b. 340 N, 270°

34. a. 51°

      b. 140 N

35. a. 150 N

      b. 220 N


36. 430 N

37. a. 284 N, 90.0°

      b. 113 N, 0.0°

      c. 1.9 m/s2, 180.0°

38. a. 111 N


      c. 100 N

      d. 0.327

39. a. 8.0 m/s2

      b. 3.2 m/s2

      c. 3.8 N

40. a. 0.176

      b. 0.867 m/s2