Question

a 1.0\, \text {kg}1.0kg1, point, 0, start text, k, g, end text cart moving right at 5.0\,\dfrac{\text m}{\text s}5.0 s m ​ 5, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction on a frictionless track collides with a second cart moving left at 2.0 \,\dfrac{\text m}{\text s}2.0 s m ​ 2, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction. the 1.0\, \text {kg}1.0kg1, point, 0, start text, k, g, end text cart has a final speed of 4.0\,\dfrac{\text m}{\text s}4.0 s m ​ 4, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction to the left, and the second cart has a final speed of 1.0\,\dfrac{\text m}{\text s}1.0 s m ​ 1, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction to the right. what is the mass of the second cart?

Answer 1

The mass of the second cart is 3.0 kg.

Step-by-step explanation:

To determine the mass of the second cart, we can use the principle of conservation of momentum. In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision. The momentum of an object is given by the product of its mass and velocity.

Let's represent the mass of the first cart as m1 and the mass of the second cart as m2. The initial momentum of the first cart is m1 * 5.0 m/s, and the initial momentum of the second cart is m2 * (-2.0 m/s) since it is moving in the opposite direction. After the collision, the final momentum of the first cart is m1 * (-4.0 m/s), and the final momentum of the second cart is m2 * 1.0 m/s.

Using the principle of conservation of momentum, we can equate the initial momentum to the final momentum:

m1 * 5.0 m/s + m2 * (-2.0 m/s) = m1 * (-4.0 m/s) + m2 * 1.0 m/s

This equation can be simplified to:

5.0 m1 - 2.0 m2 = -4.0 m1 + m2

Bringing like terms together:

9.0 m1 = 3.0 m2

Dividing both sides by 3.0:

m1 = (3.0/9.0) m2

Simplifying further:

m1 = (1.0/3.0) m2

Since we know that the mass of the first cart (m1) is 1.0 kg, we can substitute this value into the equation:

1.0 kg = (1.0/3.0) m2

Multiplying both sides by 3.0:

3.0 kg = m2

Therefore, the mass of the second cart is 3.0 kg.

Answer 2

The mass of the second cart, given that the first cart has a mass of 1.0 Kg, is 3 kg

How to calculate the mass of the second cart?

The mass of the second cart can be calculated as explained below:

• Mass of 1st cart (m₁) = 1.0 Kg
• Initial speed of 1st cart (u₁) = 5.0 m/s
• Initial speed of 2nd cart (u₂) = -2.0 m/s
• Final speed of 1st cart after collision (v₁) = -4.0 m/s
• Final speed of 2nd cart after collision (v₂) = 1.0 m/s
• Mass of 2nd cart (m₂) =?

Total momentum before = Total momentum after

`m_1u_1\ +\ m_2u_2 = m_1v_1 + m_2v_2\\\\(1\ *\ 5)\ +\ (m_2\ *\ -2) = (1\ *\ -4)\ +\ (m_2\ *\ 1)\\\\5\ -\ 2m_2 = -4\ + m_2\\\\Collect\ like\ terms\ \\\\5\ +\ 4 = m_2\ +\ 2m_2\\\\9 = 3m_2\\\\m_2 = (9)/(3) \\\\m_2 = 3\ Kg`

Therefore, the mass of the second cart is 3 Kg

Complete question:

A 1.0 kg cart moving right at 5.0 m/s on a friction-less track collides with a second cart moving left at 2.0 m/s. The 1.0 kg cart has a final speed of 4.0 m/s to the left, and the second cart has a final speed of 1.0 m/s to the right. What is the mass of the second cart? [Consider rightward as the positive direction]