Chapter 9, Problem 87A

To determine

The change in momentum and the velocity of the object.

Answer to Problem 87A

  $60\text{kg}\cdot \text{m/s}$ and $20\text{m/s}$ , respectively

Explanation of Solution

Given:

The mass of the object, $m=3.00\text{kg}$

The force applied on the object, $F=6.00\text{N}$

Time duration for which the force is applied on the object, $\Delta t=10.0\text{s}$

Formula used:

Impulse on an object is equal to the change in momentum of an object,

  $\text{Impulse}=F\Delta t=p_f-p_i$

where $F$ is the applied force for time $\Delta t$ , $p_f$ is the final momentum, $p_i$ is the initial momentum.

Momentum of an object of mass m and moving with velocity v is given by,

  $p=mv$

Calculation:

Using the given values in above formula of Impulse, the change in momentum of the object will be,

  $\begin{array}{c}F\Delta t=p_f-p_i\\ \left(6\right)\left(10\right)=\Delta p\\ \Delta p=60\text{kg}\cdot \text{m/s}\end{array}$

Then, using the formula of momentum, the change in velocity of the object will be,

  $\begin{array}{c}\Delta p=60\text{kg}\cdot \text{m/s}\\ m\Delta v=60\text{kg}\cdot \text{m/s}\\ 3\Delta v=60\text{kg}\cdot \text{m/s}\\ \Delta v=20\text{m/s}\end{array}$

Conclusion:

Thus, the change in momentum and the velocity of the object is $60\text{kg}\cdot \text{m/s}$ and $20\text{m/s}$ , respectively.