Question

determine whether the following statements are true or false.
momentum and impulse do not have the same units. true false
the si units for momentum and impulse are kg*m/s. true false
momentum and impulse are both vector quantities. true false
momentum is the change in impulse. true false

Explanation:

1. Statement: Momentum and Impulse do not have the same units.

Impulse is defined as the change in momentum, \( J=\Delta p \). By the impulse - momentum theorem, since impulse is equal to the change in momentum, they must have the same units. So the statement is false.

The formula for momentum is \( p = mv \), where mass \( m \) has units of kg and velocity \( v \) has units of \( \text{m/s} \), so momentum has units \( \text{kg}\cdot\text{m/s} \). Impulse \( J = F\Delta t \), force \( F \) has units \( \text{kg}\cdot\text{m/s}^2 \) and time \( \Delta t \) has units \( \text{s} \), so \( J \) has units \( \text{kg}\cdot\text{m/s}^2\times\text{s}=\text{kg}\cdot\text{m/s} \). So the statement is true.

Momentum \( \vec{p}=m\vec{v} \), since velocity \( \vec{v} \) is a vector, momentum is a vector. Impulse \( \vec{J}=\vec{F}\Delta t \), force \( \vec{F} \) is a vector, so impulse is also a vector. So the statement is true.

Answer:

False

2. Statement: The SI units for momentum and impulse are \( \text{kg}\cdot\text{m/s} \).