WorkEnergy_problems-solutions

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A. Work, Work-Energy theorem and Scalar Product 1. A 380-kg piano slides 3.9m down a 27 o incline and is kept from accelerating by a man who is pushing back on it parallel to the incline. Ignoring friction, Determine a) The force exerted by the man b) The work done by the man on the piano c) The work done by the force of gravity d) The net work done on the piano. Source : Question 11 Chap. 7, Physics for Scientists and Engineers , Giancoli, 4 th ed.

2. A grocery cart with mass of 16 kg is being pushed at a constant speed up a frictionless flat 12 o ramp by a force F p which acts at an angle of 17 o below the horizontal. Find the work done by each of the forces acting on the cart if the ramp is 15 m long. Source : Question 15 Chap. 7, Physics for Scientists and Engineers , Giancoli, 4 th ed. 3. What is the dot product of ࠵? ⃗ = 20࠵? ! ࠵?̂ − 4.0࠵?࠵?̂ + 5.0࠵? 0 and ࠵? 2⃗ = 11.0࠵?̂ + 2.5࠵?࠵?̂ ? Source : Question 16 Chap. 7, Physics for Scientists and Engineers , Giancoli, 4 th ed.

4. A 12.0 N force with a fixed orientation does work on a particle as the particle moves through a displacement ࠵? ⃗ = 52.00࠵?̂ − 4.00࠵?̂ + 3.00࠵? 0 7 m. What is the angle between the force and the displacement if the change in the particle’s kinetic energy is a) +30.0 J and b) -30.0 J. Source : Halliday, Resnick, and Walker chp. 7, #15, 7 th Edition. 5. The force on a particle, acting along the x -axis, varies as shown. Determine the work done by this force to move the particle along the x -axis from x = 0.0 m to x = 15.0 m. Source : Question 40 Chap. 7, Physics for Scientists and Engineers , Giancoli, 4 th ed.

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6. A 4.5-kg object moving in two dimensions initially has a velocity ࠵? " 2222⃗ = (10.0࠵?̂ + 20.0࠵?̂) m/s. A net force ࠵? ⃗ then acts on the object for 2.0 s, after which the objec’s velocity is ࠵? ! 2222⃗ = (15.0࠵?̂ + 30.0࠵?̂) m/s. Determine the work done by ࠵? ⃗ on the object. Source : Question 61 Chap. 7, Physics for Scientists and Engineers , Giancoli, 4 th ed. 7. Two forces, ࠵? " 222⃗ = 51.50࠵?̂ − 0.80࠵?̂ + 0.70࠵? 0 7 N and ࠵? ! 2222⃗ = (−0.70࠵?̂ + 1.20࠵?̂) N, are applied on a moving object of mass 2.0 kg. The displacement produced by the two forces is ∆࠵? 2222⃗ = 58.0࠵?̂ + 6.0࠵?̂ + 5.0࠵? 0 7 m. What is the total work done? Source : Question 75 Chap. 7, Physics for Scientists and Engineers , Giancoli, 4 th ed.

8. A crate of mass 10.0 kg is pulled up a rough incline with an initial speed of 1.50m/s. The pulling force is 100N parallel to the incline, which makes an angle of 20.0° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 5.00 m. a) How much work is done by the gravitational force on the crate? b) How much does the thermal energy of the system increase due to friction? c) How much work is done by the 100-N force on the crate? d) What is the change in kinetic energy of the crate? e) What is the final speed? Source : Serway chapter 7, #33. . Volume 6 a. -168J, b. 184J, c. 500J, d. 148J, e. 5.65

9. A shopper in a supermarket pushes a cart with a force of 35 N directed at an angle of 25 ° below the horizontal. The force is just sufficient to balance various friction forces, so the cart moves at constant speed. (a) Find the work done by the shopper on the cart as she moves down a 50.0-m-long aisle. (b) What is the net work done on the cart by all forces? Why? (c) The shopper goes down the next aisle, pushing horizontally and maintaining the same speed as before. If the friction force doesn’t change, would the shopper’s applied force be larger, smaller, or the same? (d) What about the work done on the cart by the shopper? Source : Serway chp. 7, #1, 9 th Edition.

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B: Conservation of Energy 10. An elevator cables break when a 925-kg elevator is 22.5 m above the top of a huge spring ( k = 8.00 x 10 4 N/m) at the bottom of the shaft. Calculate the amount the spring compresses. Source : Question 69 part c) Chap. 7, Physics for Scientists and Engineers , Giancoli, 4 th ed. 11. A vertical spring of spring constant k = 875 N/m is attached to a table and is compressed down by 0.160 m. a) What upward speed can it give to a 0.380 kg ball when released? b) How high above its original position (spring compressed) will the ball fly? Source : Question 19 Chap. 8, Physics for Scientists and Engineers , Giancoli, 4 th ed.

12. When a 4.00-kg object is hung vertically on a certain light spring that obeys Hooke’s law, the spring stretches 2.50 cm. If the 4.00-kg object is removed, (a) how far will the spring stretch if a 1.50-kg block is hung on it? (b) How much work must an external agent do to stretch the same spring 4.00 cm from its unstretched position? Source : Serway chp. 7, #17, 9 th Edition.

13. a) A roller-coaster car is pulled up to point 1 where it is released from rest. Assuming no friction, calculate is speed at points 2, 3 and 4. b) Consider that, instead, the roller-coaster passes point 1 with a speed of 1.70 m/s and that the average force of friction is equal to 0.23 of the force of gravity. With what speed will it reach point 2 if the distance traveled in 45.0 m? Source : Questions 20 (a) and 34 (b) Chap. 8, Physics for Scientists and Engineers , Giancoli, 4 th ed. 14. A skier traveling at 9.0 m/s reaches the foot of a steady upward 19 o incline and glides 12 m up along this slope before coming to rest. What was the average coefficient of friction? Source : Question 35 Chap. 8, Physics for Scientists and Engineers , Giancoli, 4 th ed.

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15. Consider the track shown. The section AB is one quadrant of a circle of radius 2.0 m and is frictionless. B to C is a horizontal span 3.0 m long with a coefficient of kinetic friction μ k = 0.25. The section CD under the spring is frictionless. A block of mass 1.0 kg is released from rest at A. After sliding on the track, it compresses the spring by 0.20 m. Determine a) The speed of the block at B. b) The thermal energy produced as the block slides from B to C. c) The speed of the block at C d) The spring constant k . Source : Question 36 Chap. 8, Physics for Scientists and Engineers , Giancoli, 4 th ed.

16. A spring ( k =75 N/m) has an equilibrium length of 1.00 m. The spring is compressed to a length of 0.50 m and a mass of 2.0 kg is placed at its free end on a frictionless slope which makes an angle of 41 o with respect to the horizontal. The spring is then released. a) If the mass is not attached to the spring, how far up the slope will the mass move before coming to a rest? b) If the mass is attached to the spring, how far up the slope will the mass move before coming to a rest? c) Now the incline has a coefficient of kinetic friction μ k . If the block, attached to the spring, is observed to stop just as it reached the spring’s equilibrium position, what is the coefficient μ k ? Source : Question 42 Chap. 8, Physics for Scientists and Engineers , Giancoli, 4 th ed.

17. A 2.0-kg block slides along a horizontal surface with a coefficient of kinetic friction μ k = 0.30. The block has a speed v = 1.3 m/s when it strikes an ideal spring head-on. a) If the spring constant is k = 120 N/m, how far is the spring compressed when the block comes to a rest? b) What minimum value of the coefficient of static friction μ s will assure that the spring remains compressed at the maximum compressed position? c) If μ s is less than this, what is the speed of the block when it detaches from the decompressing spring? Source : Question 43 Chap. 8, Physics for Scientists and Engineers , Giancoli, 4 th ed.

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18. Two objects are connected by a light string passing over a light, frictionless pulley, as shown. The object of mass m 1 = 5.00 kg is released from rest at a height h = 4.00 m above the table. Using the isolated sys- tem model, (a) determine the speed of the object of mass m 2 = 3.00 kg just as the 5.00-kg object hits the table and (b) find the maximum height above the table to which the 3.00-kg object rises. Source : Serway chp. 8, #7, 9 th Edition.

19. A bead slides without friction around a loop-the-loop. The bead is released from rest from a height of 3.5R. a) What is its speed at A? b) Find the normal force at A. Source : Serway Ch. 8, Volume 6, #5

20. A 10.0-kg block is released from point A. The track is frictionless except for the portion between points B and C, which has a length of 6.00 m. The block travels down the track, hits a spring of force constant 2250 N/m, and compresses the spring 0.300 m from its equilibrium position before coming to rest momentarily. Determine the coefficient of kinetic friction between the block and the rough surface between B and C. Source : Serway, ch 8, #57. Vol 6

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21. The coefficient of friction between the 3.00-kg block and the surface in the figure is 0.400. The system starts from rest. What is the speed of the 5.00-kg ball when it has fallen 1.50 m? Source : Serway ch 8 #31. vol 6

22. A 2.00-kg block situated on a rough incline is connected to a spring of negligible mass having a spring constant of 100 N/m. The pulley is frictionless. The block is released from rest when the spring is unstretched. The block moves 20.0 cm down the incline before coming to rest. Find the coefficient of kinetic friction between block and incline. Source : Serway 54, ch 8, vol 6

23. Two blocks are connected by a string over a massless, frictionless pulley, as shown in the figure. The inclined plane is also frictionless. The spring constant is 250 N/m. The spring is unstretched when the system is as shown in the figure. The 20.0-kg block is pulled 20.0 cm down the incline (so that the 30.0- kg block is 40.0 cm above the floor) and released from rest. Find the speed of each block when the 30.0- kg block is 20.0 cm above the floor (that is, when the spring is unstretched). Source : Serway ch 8 #59. Vol 6

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24. A roller-coaster car is released from rest at the top of the first rise and then moves freely with negligible friction. The roller coaster shown has a circular loop of radius R in a vertical plane. a) Suppose first that the car barely makes it around the loop: at the top of the loop the riders are upside down and feel weightless. Find the required height of the release point above the bottom of the loop, in terms of R . b) Now assume that the release point is at or above the minimum required height. Show that the normal force on the car at the bottom of the loop exceeds the normal force at the top of the loop by six times the weight of the car. Source : Serway ch 8. #73. Vol 6

25. A ball whirls around in a vertical circle at the end of a string. The other end of the string is fixed at the center of the circle. Assuming the total energy of the ball–Earth system remains constant, show that the tension in the string at the bottom is greater than the tension at the top by six times the ball’s normal weight ( mg ). Source : Serway chp. 8, #41, 9 th Edition.

WorkEnergy_problems-solutions

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