Physics 1120 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, F₂, and F₃ act on a particle with mass 6.0 kg. The forces are:
   F₁ = 2i - 5j + 2k,
   F₂ = -4i + 8j + 1k,
   F₃ = 5i + 2j -5k ,
   where the forces are measured in Newtons. (a) What is the net force vector? (b) What is the magnitude of the net force? (c) What is the acceleration vector? (d) What is the magnitude of the acceleration vector?

3. 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? What would have to be the magnitude and direction of a fourth force F₄ so that the acceleration of the mass would be zero?

4. 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.

5. The 80.0 kg male partner of a figure skating duo pushes his 60.0 kg female partner with a force of 70.0 N. Find the acceleration of both partners.

6. In the diagram below, an object travels over a hill, down a valley, and around the inside of a loop-the-loop. At each of the specified points draw a free body diagram indicating the directions of the normal force, the weight, and the centripetal acceleration if it exists.
   
   

7. 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.
   
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8. The apparent eight of a person in an elevator is 7/8 of his actual weight. What is the acceleration (including the direction) of the elevator?
   

9. A person is standing on a weigh scale in an elevator. When the elevator is accelerating upward with constant acceleration a, the scale reads 867.0 N. When the elevator is accelerating downwards with the same constant acceleration a, the scale reads 604.5 N. Determine the magnitude of the acceleration a, the weight of the person, and the mass of the person.
   

10. A 1200-kg elevator is carrying an 80.0-kg passenger. Calculate the acceleration of the elevator (and thus of the passenger) 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.

11. A car is traveling over the crest of a small semi-circular hill of radius R = 750 m. How fast would it have to be traveling for it to leave the ground?

12. A rollercoaster is at the inside top of a circular loop of radius R = 150 m. How fast must the rollercoaster be going if it isn't to fall off?
    
    
    

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

14. In the diagram below, block A weighs 100N. 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.
    
    

15. A bicyclist is riding on the banked curve of a circular velodrome. The radius of curvature for the bicyclist's present position is R = 355 m. The coefficient of static friction between the wheels and the path is μ_s= 0.35 . For which range of velocities will the bicyclist remain at the same height on the banked curve?
    
    

16. A block weighing 100 N is placed on a plane with slope angle 30.0° and is connected to a hanging weight of mass m by a cord passing over a small frictionless pulley as shown below. The coefficient of static friction is 0.52, and the coefficient of kinetic friction is 0.20.
    (a) Find the mass of the small block for which the 100 N block moves up the plane at constant speed, once it has been set in motion.
    (b) Find the mass of the small block for which the 100 N block moves down the plane at constant speed, once it has been set in motion.
    (c) For what range of values of m does the block remain at rest if it is released from rest?
    
    

17. A force F pushes on a 25-kg box as shown in the figure below. The coefficient of static friction between box and incline is μ_s = 0.20 . Find the range of values for which the block remains stationary.
    

18. A box of mass M rests on a ramp cart for which the coefficient of static friction is μ_s. The ramps makes an angle θ with the horizontal. The cart can be given a maximum acceleration a_max up the ramp for which the box does not slide on the level surface of the ramp cart. Determine an equation for the magnitude of this acceleration, amax, in terms of the coefficient μ_s and the angle θ. (HINT: choosing the x-axis along the incline is not your best choice here.)
    

19. What must be the acceleration of the cart pictured below in order that block A does not fall? The coefficient of friction between the block and the cart is μ_s.
    

20. Three blocks with masses 6 kg, 9 kg, and 10 kg are connected as shown below. The coefficient of kinetic friction between the 10-kg block and the table is 0.2 . Find the acceleration of the system. Find the tension in each cord.
    
    

21. Two blocks of mass m₁ and m₂ are sliding down an inclined plane making an angle θ with the horizontal. The leading block has a coefficient of kinetic friction μ_k; the trailing block has coefficient 2μ_k. A string connects the two blocks. The string makes an angle φ with the ramp. Find the acceleration of the blocks. Find the tension in the string.
    

22. If m₁ = 25.0 kg and m₂ = 12.0 kg, calculate the normal force on the bottom mass if the force, F, is (a) 100N, (b) 363N, and (c) 500N.
    

23. A 10-kg wooden block rests on a 5-kg, L-shaped piece of metal as shown below. The metal, in turn, rests on a frictionless surface. The coefficients of friction between the wood and the metal are μ_s = 0.40 and μ_k = 0.30. (a) What is the maximum force that can be applied if the 10-kg block is NOT to slide relative to the metal? (b) What is the corresponding acceleration of the piece of metal?
    

24. In the diagram below, a 10.0-kg block sits on top of a 20.0-kg block on top of a horizontal surface. The coefficients of friction between the two blocks are μ_s1 = 0.38 and μ_k1 = 0.19. The coefficients of friction between the bottom block and the surface are μ_s2 = 0.35 and μ_k2 = 0.10. (a) What is the maximum horizontal force that can be applied to the upper block such that it does not slip relative to the bottom block? What is the acceleration of the blocks? (b) What is the maximum horizontal force that can be applied to the lower block such that it does not slip relative to the upper block? What is the acceleration of the blocks?
    

25. The diagram below shows to blocks of mass M₁ = 10.0 kg and M₂ = 25.0 kg. The upper block is connected to a wall by a string. The bottom block is pulled by a force F. The coefficients of friction between the two blocks are μ_sb = 0.24 and μ_kb = 0.15. The coefficients of friction between the bottom blocks and the table are μ_st = 0.30 and μ_kt = 0.10.
    (a) Find the maximum value of F, such that the blocks do not slip. Find the tension in the string.
    (b) If F is 100 N, find the initial acceleration of the lower block. Also find the tension in the string.
    



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 block of mass M is on an incline set at angle θ and is not moving. A spring with spring constant K is connected to the upper side of the block and a fixed support rod. The coefficients of friction between the block and the incline are μ_s and μ_k. What is the expression for the minimum amount that the spring could be stretched? What is the maximum amount that the spring could be stretched?

28. Two blocks, A of mass 8 kg and B of mass 6 kg, are on flat surface. A spring with spring constant K = 1000 N/m joins them together. The coefficients of friction between the blocks and the incline are μ_s = 0.17 and μ_k = 0.12. A constant horizontal force F is pulling block A and, via the spring, block B.
     (a) How much is the spring stretched if both blocks are moving at constant velocity? What is F?
    (b) How much is the spring stretched if both blocks are accelerating at 2 m/s²? What is F?
    

Questions? mike.coombes@kwantlen.ca