Physics 1100 In-Class Problems: Newton's Laws

1. In the diagrams below, a ball is on a flat horizontal surface. The initial velocity and constant external forces acting on the ball are indicated. Describe qualitatively how motion the motion of the ball will change.

2. Three forces F₁ = (25.0N, 42.5°), F₂ = (15.5N, 215°), and F₃ = (20.5N, 155°) accelerate an 8.75 kg mass. What is the net force acting on the mass? What is the magnitude and direction of the mass's acceleration?
3. What would have to be the magnitude and direction of a fourth force F₄ in question 2 so that the acceleration of the mass would be zero?
4. A rifle bullet with a mass of 100 g leaves the rifle with a muzzle velocity of 500 m/s. If the barrel is 0.75 m long, calculate the average acceleration of the bullet. Calculate the average force that the exploding gunpowder exerts on the bullet. If the rifle has a mass of 7.50 kg, what is its average acceleration?
5. You are thrown from a bicycle and skid in a straight line to a complete stop on a rough gravel path. A measurement of the bloody skidmark reveals that it is 3.50 m long. What average force did the gravel exert on your anatomy? Assume that your mass is 70.0 kg and that your initial speed was 30 km/h.
6. The 80.0-kg male partner of a figure skating duo pushes his 60.0-kg female partner with a force of 70.0N. Find the acceleration of both partners.
7. An 800-kg artillery piece horizontally fires a 10.5-kg shell with a muzzle velocity of 450 m/s. The barrel is 3.75 m long. What is the acceleration of both?
8. If m₁ = 25.0 kg, calculate the normal force on the bottom mass if the applied force, F, is (a) 100 N, (b) 245 N, and (c) 500 N.



9. What is the normal force on the object of mass m₁ shown in the diagram? What is the acceleration of the object? In the diagram F₁ = 25 N, F₂ = 15 N, and m₁ = 20 kg.



10. A physics instructor is pulling a string with a constant force of 1.00 Newtons. The string is attached to a toy on a frictionless surface. The string makes a 50° angle with the horizontal. The toy has a mass of 0.400 kg. Find the acceleration of the toy.

    

11. Two blocks are connected by a string. The blocks have masses of 1.50 kg and 1.20 kg. The heavier block is being pulled by a force of 8.00 N at angle of 37° to the floor. Assume the floor is frictionless. Find the tension in the string between the blocks.

    

12. Two blocks are connected by strings to the ceiling as shown in the diagram below. The left block has mass m₂ = 3.35 kg. The mass of the right block m₁ is unknown. The strings make angles θ = 60° and φ = 45° with the ceiling. Find the tension in the level string connecting the blocks. Find m₁.

    

13. In the diagram below, the mass of the object is 50.0 kg. What are the tensions in the ropes?



14. The apparent weight of a person in an elevator is 7/8^th of his actual weight. What is the acceleration (including the direction) of the elevator?
15. A 1200-kg elevator is carrying an 80.0-kg passenger. Calculate the acceleration of the elevator (and hence of the partner) if the tension in the cable pulling the elevator is (a) 15,000 N, (b) 12,557 N, and (c) 10,000 N. What is the apparent weight of the passenger in each case. Assume g = 9.81 m/s².
16. A person is standing on a weigh scale in an elevator. When the elevator is accelerating upwards with constant acceleration a the scale reads 867.0 N. When the elevator is accelerating downwards with acceleration a, the scale reads 604.5 N. Determine the acceleration a, the true weight of the person, and the mass of the person.
17. In the diagram below, m = 10.0 kg, θ = 25.0°, μ_s = 0.70, and μ_k = 0.50. What is the frictional force if F is (a) 25 N, (b) 65 N, and (c) 100 N? What is the acceleration in each case?



18. (a) If m = 10.0 kg, μ_k = 0.3, and F = 50 N i, find a.

(b) If m = 10.0 kg, a = 2.5 m/s² i and F = 75 N i, find μ_k.



19. A 15.0-kg block sitting on a floor is pulled by two forces as shown in the diagram below. The block does not move. Find the type, magnitude, and direction of the frictional force acting on the block. Note F₁ = 48.0 N and F₂ = 40.0 N.

    

20. A block weighing 100 N is placed on a plane with slope angle 30.0° and is pulled by a rope which is parallel to the incline and under tension T as shown below. The coefficient of static friction is 0.52, and the coefficient of kinetic friction is 0.20.
    (a) Find the tension T for which the block moves up the plane at constant speed, once it has been set in motion.
    (b) Find the tension T for which the block moves down the plane at constant speed, once it has been set in motion.
    (c) What is the maximum value of T for which the block will remain at rest?
    (d) What is the minimum value of T for which the block will remain at rest?

    

21. In the diagram below, block A weighs 100 N. The coefficient of static friction between the block and the surface on which it rests is 0.40. Find the maximum weight w for which the system will remain in equilibrium.



22. When a force of 500 N pushes on a 25-kg box as shown in the figure below, the acceleration of the box up the incline is 0.75 m/s². Find the coefficient of sliding friction between box and incline.



23. A 20-kg box sits on an incline as shown below. The coefficient of kinetic friction between the block and incline is 0.30. Find the acceleration of the box down the incline.



24. A 5.0-kg block is on the a 20° incline. The coefficients of friction between the block and incline are μ_s = 0.52 and μ_k = 0.38.
    (a) Does the block stay in place if the block is gently placed on the incline?
    (b) If you gave the block a gentle nudge, would it slide down the incline?
    (c) What must be the minimum angle θ of the incline if the block will always slide down the incline and never stay in place?

25. A 10.0-kg block is on a tabletop. The coefficients of friction between the block and tabletop are μ_s = 0.28 and μ_k = 0.18. A string is strung over a massless pulley to a hanging mass of 2.0 kg. But the hanging block is being held to keep everything motionless.
    (a) Does the block on the tabletop move, if the hanging block is released?
    (b) How much friction is acting on the block on the tabletop?
    (c) What mass of hanging block is needed to just get the blocks to move?
    (d) Ifthere is a slight nudge given in (c), what is the acceleration of the blocks?

26. A 10-kg block is hanging from a spring with spring constant K = 1000 N/m. The spring is attached to the ceiling of an elevator. The elevator is currently moving upwards at 10 m/s and slowing down at 1.0 m/s². How much is the spring stretched?

27. A 10-kg block is sitting on a vertical spring with spring constant K = 1000 N/m. The spring is attached to the floor of an elevator. The elevator is currently moving upwards at 10 m/s and slowing down at 1.0 m/s². How much is the spring stretched or compressed? Indicate which.

Questions?mike.coombes@kpu.ca