Question

A 1.0-kg standard cart A collides with a 0.10-kg cart B. The x component of the velocity of cart A is +0.70 m/s before the collision and +0.50 m/s after the collision. Cart B is initially traveling toward cart A at 0.40 m/s , and after the collision the x component of its velocity is +1.6 m/s .

Part A: What is the x component of the change in the momentum of A?
Part B: What is the x component of the change in the momentum of B?
Part C: What is the sum of these two x components of the changes in momentum?

Answer 1

The x component of the change in momentum of cart A is -0.20 kg·m/s, while for cart B, it is +0.20 kg·m/s. The sum of these changes in momentum is 0 kg·m/s, showing conservation of momentum in the system.

Step-by-step explanation:

The student has provided information about a collision between two carts, which involves concepts of momentum and conservation of momentum from mechanics in physics.

Part A: Change in Momentum of Cart A

The x component of the change in momentum of cart A can be calculated using the formula Δp = m(v_final - v_initial), where m is mass and v is velocity. Here, Δp = 1.0 kg (0.50 m/s - 0.70 m/s) = -0.20 kg·m/s. The negative sign indicates that the momentum decreased.

Part B: Change in Momentum of Cart B

Similarly, for cart B, Δp = 0.10 kg (1.6 m/s - (-0.40 m/s)) = 0.20 kg·m/s. The positive sign signifies an increase in momentum.

Part C: Sum of Changes in Momentum

The total change in momentum for both carts is the sum of their individual momentum changes, which is -0.20 kg·m/s + 0.20 kg·m/s = 0 kg·m/s. This means that the total momentum of the system is conserved.

Answer 2

Part A

-0.2kgm/s

Part B

+0.12m/s

Part C

-0.08kgm/s

Explanation

Momentum of a body is defined as the product of mass of the body band its velocity.

Momentum = mass × velocity

Change in momentum = m(v-u)

v is the final velocity of the body

u is the initial velocity of the body.

For cart A:

Mass m = 1.0kg

Initial velocity u = +0.70m/s(velocity before collision)

Final velocity' v = +0.5m/s(velocity after collision)

∆Momentum = 1(0.5-0.7)

= 1(-0.2)

= -0.2kgm/s

The x component of the change in the momentum of A is -0.2kgm/s

For cart B:

Similarly;

∆momentum = 0.1(1.6-0.4)

∆momentum = 0.1×1.2

∆momentum = +0.12kgm/s

The x component of the change in the momentum of B is +0.12kgm/s

Part C:

The sum of these two x components of the changes in momentum = (∆momentum)A + (∆momentum)B

= -0.2+0.12

= -0.08kgm/s