Chapter 6, Problem 41RCQ

To determine

Impulses delivered, change in momentum, final speed and momenta in 3 seconds.

Solution:

1. Impulses: Block A > Block B > Block C
2. Change in momentum: Block A > Block B > Block C
3. Final velocity: Block C > Block B > Block A
4. Momenta in 3 sec: Block A > Block B > Block C

Explanation: The change in momentum depends on how much longer the force is being applied on the body. By Newton’s second law, we can find the change in momentum of the system.

Formula used:


$F= \frac{△p}{△t}$
$△p=p_f-p_i$

Given: the

Calculations:

1. Impulse = Change in momentum

1. Block A:



$△p= p_f-p_i$
$△p=p_f$
$F\times t=△p$
$100\times 3=300=△p$
$m{v}_f=△p=300$
$v_f=\frac{300}{30}=10 m/s$

2. Block B:




$\mathrm{△;}p= p_f-p_i$
$\mathrm{△;}p=p_f$

$F\times t=△p$
$75\times 3=225=△p$
$m{v}_f=△p=225$
$v_f=\frac{225}{20}=11.25 m/s$

3. Block C:




$△p= p_f-p_i$
$△p=p_f$

$F\times t=△p$
$50\times 3=150=△p$
$m{v}_f=△p=150$
$v_f=\frac{150}{10}=15 m/s$

Impulses: Block A > Block B > Block C


1. Change in momentum: Block A > Block B > Block C
2. Final velocity: Block C > Block B > Block A
3. Momenta in 3 sec: Block A > Block B > Block C

Conclusion: The force applied on the object changes the momentum of the object.