1. (36 points) A block of mass m slides from rest at the top of the inclined plane shown at a height h = 4.00 m from the top of the table. The coefficient of kinetic friction between the block and the incline plane surface is = 0.20. The angle is 30-degrees as you can see. The block reaches the end of the incline and moves through space toward the ground and hits at a horizontal distance D from the edge of the table. The height of the table top is H = 2.00 m. Please look carefully at the diagram below. The scales shown do not necessarily conform to the computed values you will obtain. Find the following:

(a) (15 points) the speed Vf at the bottom of the incline just before the block leaves that surface.

(b) (15 points) the horizontal distance D shown below.

(c) (6 points ) the total time between the beginning of the motion at the top of the incline and at the end when the block hits the ground.

 

2. (30 points)

Shown below is a conical pendulum with a bob of mass m = 80.0 kg on a wire of length L = 10.0 m making an angle of 5.00 degrees with the vertical.

(a) (10 points) What is the radius r of the horizontal circular orbit of the bob?

(b) (20 points) What is the speed v of the bob?

 

3. Extra Credit (6 points)

A block of mass m = 2.00-kg is attached to a spring of spring constant k = 490.0 N/m on a horizontal surface. The block is stretched a distance d = 0.500 m from equilibrium points at x = 0 and released from rest. The spring then moves to the left and passes through the equilibrium point x = 0. The coefficient of kinetic friction between the block and the surface is 0.100.

(a) (2)What is the work done by the spring during this motion?
(b) (2)What is the work done by friction ?

(c) (2)What is the speed of the block at the equilibrium point x = 0?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. (20 points)

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  2. (20 points)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6. (20 points)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7. ( 20 points)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8. (20 points)