Question

critical thinking worksheet: conservation of momentum
scenario:
two ice skaters push off each other on a frictionless ice rink.

• skater a: mass = 60 kg
• skater b: mass = 40 kg

before the push, they are both at rest. after pushing off:

• skater a moves to the left with a velocity of -2 m/s
• skater b moves to the right with an unknown velocity.

before push (at rest) after push (moving apart)
problem set

1. write the law of conservation of momentum in your own words.
2. calculate the momentum of skater a after the push.
3. using momentum conservation, calculate the velocity of skater b after the push.
4. who is moving faster after the push, skater a or skater b? why?

Explanation:

Step1: Recall momentum formula

The formula for momentum is $p = mv$, where $p$ is momentum, $m$ is mass and $v$ is velocity.

Step2: Calculate Skater A's momentum

Given $m_A=60$ kg and $v_A = - 2$ m/s. Using the formula $p_A=m_Av_A$, we have $p_A=60\times(-2)=- 120$ kg·m/s.

Step3: Apply conservation of momentum

The initial momentum of the system $p_{i}=0$ (since both skaters are at rest). According to the law of conservation of momentum $p_{i}=p_{f}$, so $0 = p_A + p_B$. We know $p_A=-120$ kg·m/s, then $p_B = 120$ kg·m/s. Also, $p_B=m_Bv_B$, with $m_B = 40$ kg. So $v_B=\frac{p_B}{m_B}=\frac{120}{40}=3$ m/s.

Step4: Compare velocities

The speed of Skater A is $|v_A| = 2$ m/s and the speed of Skater B is $|v_B|=3$ m/s. Since $3>2$, Skater B is moving faster.

Answer:

1. -120 kg·m/s
2. 3 m/s
3. Skater B is moving faster because the speed of Skater A is 2 m/s and the speed of Skater B is 3 m/s.