a) In your own words, define linear momentum and impulse. b) Explain the relationship between Impulse and…

Question

a) In your own words, define linear momentum and impulse. b) Explain the relationship between Impulse and change in momentum, giving one real-life example for each.

ScanSolve AI Tutor · Accepted Answer

The problem statement does not specify the mass of the second stationary ball. For this solution, it is assumed that the second ball has the same mass as the first ball, i.e., $m_2 = 0.2 \text{ kg}$ .

Identify the given values and the assumption.
- Mass of the first ball: $m_1 = 0.2 \text{ kg}$
- Initial velocity of the first ball: $u_1 = 5 \text{ m/s}$
- Initial velocity of the second ball (stationary): $u_2 = 0 \text{ m/s}$
- Assumption: Mass of the second ball: $m_2 = 0.2 \text{ kg}$
Apply the principle of conservation of linear momentum.
For an elastic collision, the total momentum before the collision equals the total momentum after the collision:
$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$
Substitute the known values:
$(0.2 \text{ kg})(5 \text{ m/s}) + (0.2 \text{ kg})(0 \text{ m/s}) = (0.2 \text{ kg}) v_1 + (0.2 \text{ kg}) v_2$ $1.0 \text{ kg} \cdot \text{m/s} = 0.2 v_1 + 0.2 v_2$
Divide the entire equation by 0.2:
$5 = v_1 + v_2 \quad (*)$
Apply the relative velocity equation for an elastic collision.
For an elastic collision, the relative speed of approach equals the relative speed of separation:
$u_1 - u_2 = v_2 - v_1$
Substitute the known values:
$5 \text{ m/s} - 0 \text{ m/s} = v_2 - v_1$ $5 = v_2 - v_1 \quad (**)$
Solve the system of equations for $v_1$ and $v_2$ .
We have two equations:
1. $v_1 + v_2 = 5$
2. $-v_1 + v_2 = 5$
Add equation (1) and equation (2):
$(v_1 + v_2) + (-v_1 + v_2) = 5 + 5$ $2v_2 = 10$ $v_2 = 5 \text{ m/s}$
Substitute the value of $v_2$ into equation (1):
$v_1 + 5 = 5$ $v_1 = 0 \text{ m/s}$
The velocities of both balls after the collision are:
- Velocity of the first ball: $\boxed{\mathbf{v_1 = 0 \text{ m/s}}}$
- Velocity of the second ball: $\boxed{\mathbf{v_2 = 5 \text{ m/s}}}$

A) In your own words, define linear momentum and impulse. b) Explain the relationship between Impulse and change in momentum, giving one real-life example for each.

Step-by-step solution

Identify the given values and the assumption.

Apply the principle of conservation of linear momentum.

Apply the relative velocity equation for an elastic collision.

Solve the system of equations for $v_1$ and $v_2$ .

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