Question

1. two lab carts are pushed towards each other from opposite ends of the track so that their velcro bumpers are facing each other. the red cart has a mass of 0.3 kg and is pushed with a velocity of +5 m/s. the blue cart has a mass of 0.5 kg and is pushed in the opposite direction with a velocity of -3 m/s. the carts stick together when they collide.

a) draw a picture showing the situation described before and after the collision. draw arrows showing the velocities of each cart.
b) calculate the total momentum of the system before the collision.
c) calculate the total momentum of the system after the collision.
d) calculate the velocities of the carts after the collision.

Explanation:

Step1: Calculate total momentum before collision

The formula for momentum is \(p = mv\). For the red cart \(m_1 = 0.3\space kg\), \(v_1=+ 5\space m/s\), so \(p_1=m_1v_1=(0.3)(5)=1.5\space kg\cdot m/s\). For the blue cart \(m_2 = 0.5\space kg\), \(v_2=-3\space m/s\), so \(p_2=m_2v_2=(0.5)(- 3)=-1.5\space kg\cdot m/s\). The total momentum before collision \(p_{total - before}=p_1 + p_2\).

$$p_{total - before}=1.5+( - 1.5)=0\space kg\cdot m/s$$

Step2: Calculate total momentum after collision

According to the law of conservation of momentum \(p_{total - after}=p_{total - before}\). So \(p_{total - after}=0\space kg\cdot m/s\)

Step3: Calculate velocity after collision

Since \(p = mv\) and \(p_{total - after}=(m_1 + m_2)v_{after}\), and \(m_1 + m_2=0.3 + 0.5=0.8\space kg\), \(p_{total - after}=0\). Then \(v_{after}=\frac{p_{total - after}}{m_1 + m_2}\)

$$v_{after}=\frac{0}{0.8}=0\space m/s$$

Answer:

b) \(0\space kg\cdot m/s\)
c) \(0\space kg\cdot m/s\)
d) \(0\space m/s\)