Question

Answer all parts. Write big, clear and legibly.  

A 0.10kg dart is fired horizontally at the center of a 0.80kg vertically hanging block, sticking to it. The system reaches a maximum height, h, of 0.20m above the collision point.

Find:

a) the velocity of the dart – block system just after the collision

b) the velocity of the dart before collision

c) the energy lost during the collision.

d) if the dart gains its speed due to a spring system that is initially compressed 0.05m from its equilibrium

position, determine the spring constant.

e) If the dart didn’t stick to

the block, but instead fell vertically after collision, would the initial velocity of the

dart have to be greater, less than, or equal to the velocity that was found in part (b)? Justify.

Answer 1

Given

M₁=0.10Kg

M₂=0.80Kg

h=0.20m

The potential energy of the system at height is given by

a)

From the conservation of energy, we get

or,

or,

or,

therefore the velocity of the dart – block system just after the collision is 1.98m/s

b)Let the velocity of the dart before the collision is V_d

Therefore

or,

or,

c)

the energy lost during the collision is given by

or,

d) given

from the conservation of energy, we get

or,

or,

e)

Let

If the dart didn’t stick to the block but instead fell vertically after a collision, the initial velocity of the dart would be V_d^'

^{so from the conservation of momentum, we get}

^or,

therefore If the dart didn’t stick to the block, but instead fell vertically after a collision, the initial velocity of the

dart has to be less than to the velocity that was found in part (b)