Chapter 4 Work and Energy
4-1. Two forces, F1?(1.5i?0.80j?0.70k)N and F2?(?0.70i?1.20j)N
are applied on a moving object of mass 0.2kg. The displacement vector ????produced by the two forces is d?(8.0i?6.0j?5.0k)m (a) what is the work
??done by the two forces?(b) if there is a frictional force given by Ffr??F1 what is the net work done?
4-2. A varying force is given by F?Ae?kx, where x is the position, A and k are constants that have units of N and m-1, respectively. What is the work done by the force when x goes from 0.10m to infinity?
??344-3. A particular spring obeys the force law F?(?kx?ax?bx)i. (a) Is this
???????conservative? Why or why not. (b) If it is conservative, determine the form of the potential energy function.
4-4. The position of a 280-g object is given (in meters) by x?5.0t3?8.0t2?30t, where t is in seconds. Determine the net rate of work done on this object (a) at t=2.0s and (b) at t=4.0s. (c) What is the average net power input during the interval from t=0s to t=2.0s, and in the interval from t=20.s to t=4.0s. 4-5. In Fig , a block of mass m=12 kg is released from rest on a frictionless incline of angle ??300 . Below the block is a spring that can be compressed 2.0cm by a force of 270N. The block momentarily stops when it compresses the spring by 5.5cm.
(a) How far does the block move down the incline from its rest postion to the sttopping point?
(b) what is the speed of the block just as it touches the spring?
m?
4-6 Two blocks, of masses M=2.0kg and 2M, are connected to a spring of spring constant k=200N/m that has one end fixed, as shown in Fig. The horizontal surface and the pulley are frictionless, and the pulley has
negligible mass. The blocks are released from rest with the spring relaxed. (a) What is the combined kinetic energy of the two blocks when the hanging block has fallen 0.090m? (b) What is the kinetic energy of the hanging block when it has fallen that 0.090m?(b)What maximum distance does the hanging block fall before momentarily stopping?
M2M
Ans:
4-1. (a) 12.3J (b) 1.6 J 4-2. W?A?0.1ke k
1214154-3 . (a) Yes！ (b) U?kx2?ax4?bx5?constant 4-4 (a) -24.6W (b) 4.3?103W
(c) From t = 0 to t = 2.0 s, we have P= – 62.7 W.
From t = 2.0 s to t = 4.0 s, we have P = 1.5?103 W.
4-5 0.35m
4-6 (a) 2.7J (b) 1.8J (c) 0.39m
