A pinball machine is 2m long and inclined 20? to the horizontal. A 50 g ball is at rest on a ball shooter with stiffness k = 42 N/m. Thecoefficient of friction between the ball and the table is μ = 0.05.a) By how much do you need to displace the ball shooter if you wantthe velocity of the ball at the top of the pinball machine to be2m/s?b) What is the acceleration of the ball?c) What is the work done by friction?d) How long does it take for the ball to reach the top?e) Compute the power of friction.

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Some Problems on Work
1. Joe is pulling a box of mass m = 10 kg up an inclined surface (?= 30degrees) using
a rope. The coefficient of kinetic friction between the surface andthe box is
Âµk = 0.5. It takes 10 seconds for Joe to bring up a box at aconstant velocity
V = 0.8m=s.
(a) What is the tension of the rope?
(b) What is the work done by the tension?
(c) What is the work done by the normal force?
(d) What is the work done by gravity?
(e) What is the total work done on the box?
(f) What is the power output necessary to Joe to bring up thebox?
maximal compression of the spring?
2. A block (m=50 kg) slides down a 3 m long inclined surface (? =30). The
coefficient of kinetic friction between the block and the surfaceis Âµk = 0.3.
Calculate the nal velocity of the block using the work-energytheorem.
3. A pendulum of length l and mass m is released from rest at anangle ? from
the equilibrium position.
(a) Neglect air friction. Calculate the velocity of the pendulumwhen the angle
is zero. Express your result in terms of ?, l, and m.
(b) Suppose ? = 60 degrees and l = 1 m. Suppose that the velocityof the pendulum
when the angle is zero is 1 m/s. Calculate the work done by the airfriction.
4. A point particle of mass m = 20 g is moving on a
at
surface when it reaches a slope which brigs it up by h = 08 m. Thespeed of
the particle in position A is v = 5 m/s.
(a) Suppose that there is no friction. What is the velocity of theparticle when
it reaches position B?
(b) Suppose that there is friction, and that the velocity of theparticle in B is
0. What is the work done by the friction from A to B?
5. A ball is shoot vertically with initial speed v, from a
table of height h.
(a) Calculate the maximal height ymax that the ball can reach (b)Calculate the velocity of the ball just before it hits thefloor.

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