How to Calculate Total Momentum of Two Carts in Motion
What is the total momentum of the system of the two carts at a certain instant before they collide?
Data: Mass of first cart (m₁) = 2.9 kg Mass of second cart (m₂) = 1.4 kg Velocity of first cart (v₁) = +3.9 m/s Velocity of second cart (v₂) = -1.2 m/s
What was the velocity of the first cart when the second cart was still at rest?
Total Momentum Calculation:
The total momentum of the system of the two carts at a certain instant before they collide can be calculated using the formula:
p = m₁v₁ + m₂v₂
Substitute the given values:
m₁ = 2.9 kg, v₁ = +3.9 m/s
m₂ = 1.4 kg, v₂ = -1.2 m/s
Calculating the total momentum:
p = 2.9 × 3.9 + 1.4 × (-1.2)
p = 9.63 kg m/s
Velocity Calculation:
To find the velocity of the first cart when the second cart was at rest, we can use the formula:
v₁ = (p - m₂v₂) / m₁
Substitute the known values:
p = 9.63 kg m/s, m₁ = 2.9 kg, m₂ = 1.4 kg, v₂ = 0 m/s
Calculating the velocity:
v₁ = (9.63 - 1.4 × 0) / 2.9
v₁ = 3.32 m/s
In this example, we looked at the scenario of two carts with masses of 2.9 kg and 1.4 kg, respectively. The carts were moving towards each other on a frictionless, horizontal track and were loaded with magnets that attracted each other, causing their speeds to increase.
The total momentum of the system of the two carts before they collided was found to be 9.63 kg m/s. This was calculated by summing the individual momentums of each cart, taking into account their masses and velocities.
Additionally, we determined that the velocity of the first cart when the second cart was at rest was 3.32 m/s. This was found by applying the principle of conservation of momentum and solving for the unknown velocity using the total momentum of the system and the initial conditions.
Understanding the concepts of momentum and velocity in a system of interacting objects is crucial in various physics problems, especially those involving collisions or interactions between multiple moving bodies.