a block with a mass of 2.5 kg starts from rest at the top of the apparatus shown

Question

a block with a mass of 2.5 kg starts from rest at the top of the apparatus shown below. it then slides without friction down the incline, and collides with a spring attached to a wall. The spring has a spring constant of K=120N/m. Using the principle of energy conservation,

a. find the initial gravitational potential energy of the block at point A

b. find the kinetic energy of the block at point B

c. what is the velocity of the block at point C?

d. what is the maximum compression of the spring when it is hit by the block?

a block with a mass of 2.5 kg starts from rest at the top of the apparatus shown below. it then slides without friction down the incline, and collides with a spring attached to a wall. The spring has a spring constant of K=120N/m. Using the principle of energy conservation, a. find the initial gravitational potential energy of the block at point A b. find the kinetic energy of the block at point B c. what is the velocity of the block at point C? d. what is the maximum compression of the spring when it is hit by the block?

Explanation / Answer

a)

Gravitational potential energy = mgh = 2.5*9.8*1.2 = 29.4 J

b)

0.5mv^2 = mgh

   v = sqrt [2gh] = sqrt [ 2 * 9.8 * 8 ] = 12.5 m/s

c)

The total gravitational potential energy at B is entirely converted into kinetic energy, so

v = 12.5 m/s

d)

0.5mv^2 = 0.5kx^2

   x = sqrt [mv^2/k]

= sqrt [2.5 * 12.5^2 / 120]

   = 1.8 m

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