Exploring Momentum: Calculating Total Momentum and Velocities of Carts
What is the total momentum of the system of the two carts at a certain instant? What was the velocity of the first cart when the second cart was still at rest?
Total Momentum Calculation
To find the total momentum of the system of the two carts at the given instant, we calculate the momentum of each cart separately and then add them together.
The mass of the first cart is 2.6 kg, and its velocity is +3.7 m/s. Therefore, momentum of the first cart is calculated as:
Momentum of first cart = mass × velocity
Momentum of first cart = 2.6 kg × 3.7 m/s
Momentum of first cart = 9.62 kg·m/s (rounded)
The mass of the second cart is 1.5 kg, and its velocity is -2.9 m/s (moving in the opposite direction). The momentum of the second cart is calculated as:
Momentum of second cart = mass × velocity
Momentum of second cart = 1.5 kg × (-2.9 m/s)
Momentum of second cart = -4.35 kg·m/s (rounded)
Total momentum of the system = Momentum of first cart + Momentum of second cart
Total momentum of the system = 9.62 kg·m/s + (-4.35 kg·m/s)
Total momentum of the system = 5.27 kg·m/s (rounded)
Therefore, the total momentum of the system of the two carts at this instant is 5.27 kg·m/s.
Velocity Calculation
According to the conservation of momentum, the total momentum of an isolated system remains constant when no external forces act on it.
At the instant when the second cart is at rest, its momentum is zero. Therefore, the total momentum of the system is solely determined by the momentum of the first cart.
Total momentum of the system = Momentum of first cart
0 = 2.6 kg × velocity of the first cart
velocity of the first cart = 0 / 2.6 kg
velocity of the first cart = 0 m/s
Hence, the velocity of the first cart when the second cart was still at rest is 0 m/s.