Question:

A 0.2 kg object is moving with a velocity of 10 m/s to the right when it collides with a stationary 0.5 kg object. After the collision, the 0.2 kg object is moving with a velocity of 6 m/s to the right. Assuming the collision is perfectly elastic, what is the final velocity of the 0.5 kg object after the collision?

Answer:

Impulse can be defined as the change in momentum of an object. It can be calculated by multiplying the force applied on an object by the time it is applied. The principle of conservation of momentum states that the total momentum of a system before a collision is equal to the total momentum of the system after the collision, provided no external forces act on the system.

Let's solve the problem step-by-step:

Given data: Mass of object 1 ($m_1$) = 0.2 kg Initial velocity of object 1 ($v_{1i}$) = 10 m/s to the right Mass of object 2 ($m_2$) = 0.5 kg Final velocity of object 1 ($v_{1f}$) = 6 m/s to the right

First, we need to find the initial momentum of object 1 and the final momentum of object 1.

The initial momentum of object 1 can be calculated using the formula:

Initial momentum ($p_{1i}$) = mass of object 1 ($m_1$) x initial velocity of object 1 ($v_{1i}$)

Substituting the given values, we get:

$p_{1i}$ = 0.2 kg x 10 m/s = 2 kg*m/s to the right (positive direction)

The final momentum of object 1 can be calculated using the formula:

Final momentum ($p_{1f}$) = mass of object 1 ($m_1$) x final velocity of object 1 ($v_{1f}$)

Substituting the given values, we get:

$p_{1f}$ = 0.2 kg x 6 m/s = 1.2 kg*m/s to the right (positive direction)

According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. So,

Total initial momentum = Total final momentum

$p_{1i} + p_{2i} = p_{1f} + p_{2f}$

Since object 2 is initially at rest ($v_{2i}=0$), its initial momentum is zero, and we can simplify the equation to:

$p_{1i} = p_{1f} + p_{2f}$

Replacing the values, we get:

2 kgm/s to the right = 1.2 kgm/s to the right + $p_{2f}$

Now, let's solve for the final momentum of object 2 ($p_{2f}$):

$p_{2f}$ = 2 kgm/s to the right - 1.2 kgm/s to the right

$p_{2f}$ = 0.8 kg*m/s to the right

Finally, to find the final velocity of object 2 ($v_{2f}$), we can use the formula:

Final velocity of object 2 = Final momentum of object 2 / Mass of object 2

$v_{2f}$ = $p_{2f}$ / $m_2$

Substituting the values, we get:

$v_{2f}$ = 0.8 kg*m/s to the right / 0.5 kg

$v_{2f}$ = 1.6 m/s to the right

Therefore, the final velocity of object 2 after the collision is 1.6 m/s to the right.