Question

A dart with mass md is launched toward a block of mass mb that is suspended from a string of length L. The dart is moving horizontally with speed v immediately before it strikes the block and remains embedded. The dart-block system then swings up to a point at which its center of mass reaches a maximum height H above its starting position, as shown at right above. The block’s mass mb is greater than the dart’s mass md.
(a) Indicate which object, the dart or the block, if either, experiences an impulse of larger magnitude during the collision. If the impulse is the same magnitude for both objects, state this explicitly. Briefly explain your reasoning.
(b) If the speed of the dart as it embeds itself into the block is greater than v, how would the maximum height reached by the center of mass of the dart-block system compare to H ? Explain your response without deriving or manipulating equations.

Answer 1

Answer:

A) Impulse is the same for both the objects

B) The higher is the speed, the greater will be the height.

Explanation:

Part a)

The time of interaction of the two bodies i.e the hanging mass and the stick is same. Thus, force caused by dart on the block = force caused by block on the dart. Hence, impulse is the same for both the objects.  

Part B

The energy will be conserved in the entire reaction process

Hence, Kinetic energy = potential energy

0.5Mv^2 = gh(md+mb)

H is directly proportional to the square of speed.  

Hence, the higher is the speed, the greater will be the height.