Forces – In-Class Practice (This is not homework!)

1. A freefalling 75.0 kg skydiver is pulled by how much gravitational force?

2. Determine the net force acting on the fan cart based on measurements of its mass and the time it takes to travel a known distance starting from rest. Is the net force equal to the thrust produced by the fan?

3. A 15.0 kg object experiences a single force of 25.0 N, 30.0° (assume there is no gravity).
(a) What is the acceleration of the object? (b) What additional force would be required to cause its acceleration to be zero?

4. Two forces act on a 20.0 kg object (assume there is no gravity): F₁ = 40.0 N, 180.0° and F₂ = 75.0 N, 0.0°. Determine its acceleration.

5. Two forces act on a 5.00 kg object (assume there is no gravity): F₁ = 300 N, 90.0° and F₂ = 150 N, 0.0°. Determine its acceleration.

6. A student lifts a book bag with mass 2.50 kg. The force of gravity on the bag is 24.5 N. What force must the student exert on the bag so that: (a) it accelerates 2.00 m/s², 90.0°, and (b) it moves with constant velocity 1.00 m/s, 90.0°.

7. A certain climbing rope can exert a force of up to 4.5 kN without breaking (its tensile strength). What is the maximum upwards acceleration the rope can produce with a 50 kg climber attached at the end? Repeat for a 100 kg climber attached.

8. Determine the acceleration of the space shuttle at liftoff. The space shuttle’s mass at liftoff: orbiter = 79000 kg, external tank = 756000 kg, solid rockets = 590000 kg each (× 2). The engines produce thrust as follows: main engines = 1.67 MN each (× 3), boosters = 11.8 MN each (× 2).

9. A junkyard crane lifts and lowers a smashed car. Suppose the mass of the car is 2000 kg. Find the tension in the cable when the car: (a) accelerates 2.00 m/s², 90.0°, (b) accelerates 1.00 m/s², 270.0°, and (c) rises at a constant 2.00 m/s, 90.0°.

10. A balloon is released from the ceiling and falls to the floor. Determine the average force of friction (air resistance) acting on the balloon based on measurements of its mass and of the time and distance of the fall.

11. An 85.0 kg parachutist falls from an airplane. The table below shows an “account” of the fall. Determine the 5 values missing from the table. Note: the first missing value is an instantaneous value – the others are average or constant values found “between” two points in time.

time (s)	speed (m/s)	acceleration (m/s^2)	air resistance (N)	description:
0.00	0.00	9.8 down	0	man drops from plane
5.00	36.0		535 up	falling through air
15.0	45.0			reaches terminal velocity
		0		falling fast!
20.0	45.0			pulls “rip cord”
				chute is opening
22.0	5.00			chute is completely open
		0		falling slow!
25.0	5.00			continues to drift down

12. Aboard the space shuttle, a “floating” and “weightless” 95 kg astronaut pushes a “floating” and “weightless” 150 g notepad with a force of 5.0 N, 10.0°. Determine the acceleration of both the notepad and the astronaut.

13. Use a ranging device to measure the motion of a book that falls and is caught by a student. Determine the force of the book on the student’s hands.

14. A 2.00 kg book rests on a level table. Determine the normal force acting on the book.

15. A person applies a force of 10.0 N downward on the top of the same 2.00 kg book. Determine the normal force acting on the table in this situation.

16. A person with mass 80.0 kg is in contact with the floor. Determine the normal force acting on the person in each of the following circumstances: (a) Person stands at rest. (b) Person is pulled upward by a rope exerting 100 N of force (but remains at rest). (c) Person jumps upward with acceleration 1.00 m/s².

17. A stack of two boxes is lifted by a person. The top box is 1.00 kg and the bottom box is 10.0 kg. The person applies force to the bottom box, which causes both boxes to accelerate upwards at 2.00 m/s². (a) Determine the force of the top box acting on the bottom box. (b) Determine the applied force.

18. Given the mass, m, and the angle, θ, determine the tension in the cable and the force of the ball acting on the rod.

19. What amount of force is needed to push a 250 N crate at constant velocity across a floor where μ = 0.175? What would be the deceleration rate of the crate if you stopped pushing it?

20. Find the minimum stopping distance for a 1500 kg car traveling 29 m/s given coefficients of friction for tire on pavement: μ_s = 1.0, μ_k = 0.80. What must be true of the braking in order to achieve this?

21. Using the same coefficients from the previous problem, determine the maximum possible forward acceleration of a kid running on dry pavement.

22. A horizontal cable is used to pull the top beam from a stack of steel beams that each weigh 9.0 kN. The tension in the cable is gradually increased until the beam moves. Find its acceleration at the instant it starts to move. For steel on steel: μ_s = 0.74, μ_k = 0.57

23. Two men are initially standing at rest on a frozen lake. The larger man, mass 100.0 kg shoves the smaller man, mass 70.0 kg with a force of 150 N, 0.0°. Determine the acceleration of each person as this force is being applied. The coefficients of friction for both men are: μ_s = 0.20, μ_k = 0.10. Repeat for a shove of 80 N and of 250 N.

24. Suppose you press a 15 N book against a wall and hold it in place. If the coefficient of static friction for the book against the wall or your hand is 0.30, determine the force you must exert to keep the book from sliding down.

25. A mass, m, is supported by two strings as shown above. Measure the angle θ and the tension in one of the two strings. Use these values to determine the mass and the other tension value.

26. A 35.0 kg lawn mower is pushed across a level lawn in a direction of 0.0°. The force exerted on the handle is 100 N, 310.0°. Assume friction is negligible. (a) Determine the acceleration. (b) Determine the normal force acting on the lawn mower.

27. Two identical masses are attached to strings which pass over pulleys and support a third mass as shown in the above diagram. Given the value of the mass M and the angle θ, determine the tension in each string and the value of m.

28. A 6.00 kg box is pulled across a level floor by a rope that exerts a force of 40.0 N, 30.0°. The coefficient of sliding friction is 0.25. Determine the acceleration rate of the box.

29. A small toy car is released from rest and rolls down a ramp. Assuming the coefficient of friction is small, estimate the time for the car to roll down the ramp based on measurements of its mass and the length and angle of incline of the ramp.

30. Determine the mass needed on the end of the string in order to pull the cart up the ramp at a constant velocity as shown in the above diagram. Base your answer on measurements of the cart’s mass, the angle of incline, and the coefficient of friction.