Kinetic Energy and Work concept

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I need help with these problems.

 

1. Calculate the work done by the spring force, when a horizontal spring is released from its maximum compression position xmax up to the equilibrium position. k=1000 N/m and xmax= 10 cm.

 

2. A 5 kg box slides on a horizontal frictionless table and collides with a 2kg box initially at rest. The speed of the 5kg box is 3m/s just before the collision. If the 2 boxes stick together, what is their kinetic energy just before they strike the floor 0.5 m below the table's surface? Use energy concepts.

 

3. A 1kg block is dropped onto a relaxed vertical spring that has a constant k = 1000 N/m. The block compresses the spring by 10 cm. While the spring is being compressed:

a) what is the work done on the block by the gravitational force?

;) what is the work done on the block by the spring force?

c) what is the speed of the block just before it hits the spring?

d) After being compressed the spring is released, and the block jumps from the release point to a maximum height Hmax. Calculate Hmax.

 

4. A pendulum of length L = 2m, mass m = 1kg, is released from rest, when the cord makes an angle of 45 degrees with the vertical.

a) What is the velocity of the pendulum at the bottom?

:eek: What is the tension in the cord at the bottom?

c) What minimum velocity v0 should we give initially to the pendulum, in order to make it to swing down to the bottom and then up to the horizontal position?

 

5. 2 blocks of masses m1 = 2kg and m2 = 4kg are released at the same time, from rest, at a height of 5 m on a frictionless track and undergo an elastic hed-on collision.

a) Calculate the velocity of each block just before collision.

Calculate the velocity of each block immediately after the collision.