Question

A 0.50-kg red cart is moving rightward with a speed of 50 cm/s when it collides with a 0.50-kg blue cart that is initially at rest. After the collision, the blue cart begins moving rightward with a speed of 40 cm/s. The red cart is still moving rightward but has slowed down to a speed of 10 cm/s. Enter the momentum values (in kg•cm/s) of each individual cart and of the system of two carts before and after the collision. Also indicate the change in momentum of each cart.

Answer 1

Explanation:

Step one:

given data

mass of red cart m1=0.5kg

initial velocity u1 of red cart=50cm/s

mass of blue cart m2=0.5kg

initial velocity u2 of blue cart= 0cm/s

final velocity v2 of blue cart= 40cm/s

final velocity v1 of red cart= 10cm/s

Step two:

Momentum values red cart before and after the collision.

Before collision

P1=m1u1

P1=0.5*50

P1=25kg•cm/s

After collision

P2=m1v1

P2=0.5*10

P2=5kg•cm/s

Change in momentum= P1-P2=25-5= 20kg•cm/s

Momentum values blue cart before and after the collision.

Before collision

P1=m1u1

P1=0.5*0

P1=0 kg•cm/s

After collision

P2=m1v1

P2=0.5*40

P2=20kg•cm/s

Change in momentum= P1-P2=0-20= -20kg•cm/s

Answer 2

The total momentum of the system of the carts before collision is 25 kgcm/s.

The total momentum of the system of the carts after collision is 25 kgcm/s.

The change in momentum of the red cart is -20 kgcm/s.

The change in momentum of the blue cart is 20 kgcm/s.

The given parameters;

• mass of the red cart, m₁ = 0.5 kg
• initial speed of the red cart, u₁ = 50 cm/s
• mass of the blue cart, m₂ = 0.5 kg
• initial velocity of the blue cart, u₂ = 0
• final velocity of the blue cart, v₂ = 40 cm/s
• final velocity of the red cart, v₁ = 10 cm/s

The momentum of the red cart before collision is calculated as follows;

$P_r_1 = m_1u_1\\\\P_r_1 = 0.5 \times 50\\\\P_r_1 = 25 \ kgcm/s$

The momentum of the blue cart before collision is calculates as follows;

$P_b_1 = m_2 u_2\\\\P_b_1 = 0.5 \times 0\\\\P_b_1 = 0 \ kgcm/s$

The momentum of the red cart after collision is calculated as follows;

$P_r_2 = 0.5 \times 10\\\\Pr_2 = 5 \ kgcm/s$

The momentum of the blue cart after collision is calculated as follows;

$P_2b_2 = 0.5 \times 40\\\\P_2b_2 = 20 \ kgcm/s$

The total momentum of the system before and after collision is calculated as follows;

$P_1 = 25 \ kgcm/s \ + \ 0 = 25 \ kgcm/s\\\\P_2 = 5 \ kgcm/s \ + \ 20 \ kgcm/s = \ 25 \ kgcm/s$

The change in momentum of the red cart is calculated as follows;

$\Delta P_r = Pr_2 - Pr_1\\\\\Delta P_r = 5 - 25 = - 20 \ kgcm/s$

The change in momentum of the blue cart is calculated as follows;

$\Delta P_b = P_b_ 2 - P_b_1\\\\\Delta P_b = 20 - 0 \ = \ 20 \ kgcm/s$

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