Unit 4: Linear Momentum
Weightage : 15-25%
A ball is traveling through the air as represented by the initial momentum vector shown above on the left. A racket then makes contact with the ball, as shown in the middle figure above. After the racket makes contact with the ball, the ball is traveling through the air as represented by the momentum vector shown above on the right.
Which of the following vectors could represent the impulse the racket exerts on the ball?
Correct Answer: \( \boxed{\mathrm{A}} \)
The impulse exerted on the ball equals its change in momentum:
\(\vec{J}=\Delta\vec{p}=\vec{p}_{f}-\vec{p}_{i}\)
The initial momentum points down and to the left, while the final momentum points down and to the right.
Subtracting the initial momentum vector from the final momentum vector is equivalent to adding a vector that points up and to the right to the final vector.
The vertical components largely cancel, while the horizontal component is directed to the right.
Therefore, the impulse exerted by the racket is directed to the right.
Hence, the correct answer is (A).
A stationary golf ball is hit by a club. While the club is in contact with the ball, the ball compresses, the club exerts maximum force when the ball is at maximum compression, and then the ball expands. The momentum of the golf ball after contact with the club is represented by the vector above.
Which of the following groups of vectors could represent the force exerted on the ball at the three moments described?
Correct Answer: \( \boxed{\mathrm{A}} \)
While the club is in contact with the golf ball, the ball behaves like a compressed spring.
Initially, as the ball begins to compress, the contact force increases.
At maximum compression, the restoring force reaches its maximum value.
As the ball expands and loses contact with the club, the force decreases back toward zero while remaining directed to the right, the same direction as the ball’s final momentum.
Therefore, the force vectors should point to the right with magnitudes that increase, reach a maximum, and then decrease.
Only choice (A) shows this pattern.
Which of the following is equivalent to a unit of momentum?
Correct Answer: \( \boxed{\mathrm{D}} \)
Linear momentum is defined as
\(p=mv\)
The SI unit of momentum is
\(\mathrm{kg\cdot m/s}\)
Since
\(1~\mathrm{N}=1~\mathrm{kg\cdot m/s^{2}}\),
multiplying by seconds gives
\(1~\mathrm{N\cdot s}=1~\mathrm{kg\cdot m/s}\),
which is exactly the SI unit of momentum.
Therefore, the correct answer is (D).
