Question

A hockey ball of mass $100 g$ traveling at $10 m/s$ is struck by a hockey stick to return it along its original path with a velocity of $5 m/s$. Calculate the change of momentum which occurred in the motion of the hockey ball by the force applied by the hockey stick:
A) $1.5kgm{s^{ - 1}}$
B) $5kgm{s^{ - 1}}$
C) $1kgm{s^{ - 1}}$
D) $All$

Answer 1

Hint: Momentum is the mass content of the motion. The momentum of a body depends only on two variables i.e. mass and velocity. It is the product of the mass of the object and its velocity. Momentum is a vector quantity so; the direction of motion needs to be considered properly here.

Complete step by step solution:
Here it is given that the hockey ball of mass 100g is initially moving along a particular direction with some initial velocity. Now in its path it was hit by a hockey stick with some force. This force was strong enough to change the direction of the ball and change its velocity now the ball is moving in the direction it was coming from and now it has a final velocity of 5m/s. Here the change in momentum of the ball is needed to be calculated.
Here as the ball is initially moving with some initial velocity so it'll be having some initial momentum.
Now after the collision, the direction of the ball is reversed and velocity is also decreased hence its momentum will also be decreased.
Here we need to calculate the difference in momentum in these two cases.
As we know the momentum of a body is given as
\[p = mv\]
Let us consider the first case before the collision
Here the mass of the ball is 100g
We need to convert that into Kg
$\because 1Kg = 1000g$
$\therefore 100g = 0.1Kg$
The velocity of the object is given to be $10m{s^{ - 1}}$
So initial momentum will be
$p = 0.1 \times 10$
$ \Rightarrow {p_i} = 1kgm{s^{ - 1}}$
Now the momentum when the ball was struck by the stick
Mass of the all will be the same but now as we know momentum is a vector quantity and it considers momentum as well and, in this case, the bass is traveling in opposite direction i.e the direction it was initially coming from so here velocity will have a negative sign.
Final momentum will be
$\Rightarrow p = 0.1 \times \left( { - 5} \right)$
$\Rightarrow {p_f} = - 0.5kgm{s^{ - 1}}$
Here it is asked for a change in momentum so the change in momentum is given by
 $\Rightarrow \Delta p = {p_f} - {p_i}$
$\therefore \Delta p = - 0.5 - 1$
$\Rightarrow \Delta p = - 1.5kgm{s^{ - 1}}$
Here the minus sign denotes the change in momentum in the direction opposite to the direction of initial momentum of the ball.

Final answer is A, The change in the momentum will be $ - 1.5kgm{s^{ - 1}}$.

Note: As the momentum is a vector quantity so the direction and the signs are to be taken care of.
Momentum is always conserved in every collision here also after hitting the ball some momentum transfer was also would have been in the stick but in this question, we are only concentrating on the ball.
The force by which the ball was stuck by stick fat first stopped the ball and then imparted it a force to go in the opposite direction.