Question

1. A4-kg ball has a momentum of 12 kg m/s. What is the ball's speed?
Ap
124
C22 A swimmer with a mass of 75 kg dives off a raft with a mass of 500 kg. If the swimmer's speed is 4 m/s
immediately after leaving the raft, what is the speed of the raft?
HINT" The swimmer and raft start off as one combined mass and then separate.
- After colliding, two objects stick together and have a single velocity. Identify the type of collision.
Trelastic

Answer 1

1) The ball's speed is 3 m/s

2) The final speed of the raft is 0.6 m/s

3) The collision is inelastic

Explanation:

1)

The momentum of an object is given by

$p=mv$

where

p is the momentum

m is the mass of the object

v is its velocity

For the ball in this problem we have:

p = 12 kg m/s

m = 4 kg

Solving for v, we find its velocity (and so its speed):

$v=\frac{p}{m}=\frac{12}{4}=3 m/s$

2)

We can solve this part by applying the law of conservation of momentum: in fact, the total momentum of an isolated system (=no external forces) must be conserved. Therefore we can write:

$p_i = p_f$ (1)

where

$p_i = 0$ is the total initial momentum (the swimmer and the raft are at rest at the beginning)

$p_f = mv + MV$ is the total final momentum, where

m = 75 kg is the mass of the swimmer

M = 500 kg is the mass of the raft

v = 4 m/s is the final velocity of the swimmer

V is the final velocity of the raft

And substituting into (1) we find:

$0=mv+MV\\V=-\frac{mv}{M}=-\frac{(75)(4)}{500}=-0.6 m/s$

Where the negative sign indicates that the raft moves in the opposite direction to the swimmer: so, the speed of the raft is 0.6 m/s.

3)

In a collision between two objects, if the system is isolated the total momentum of the system is always conserved during the collision. However, this is not true for the total kinetic energy: in fact, due to the presence of internal frictions, part of the kinetic energy can be converted into thermal energy or other forms of energy.

Therefore, there are two types of collision:

- Elastic collision: in an elastic collision, also the total kinetic energy of the objects is conserved

- Inelastic collision: in an inelastic collision, the total kinetic energy is not conserved. The most extreme case is the perfectly inelastic collision, in which the two objects stick together after the collision, and in this case there is the maximum loss of kinetic energy.

Since in this problem the two objects stick together, the collision is inelastic.

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