Question

a small, 300 g cart is moving at 1.20 m/s on a frictionless track when it collides with a larger, 4.00 kg cart at rest. after the collision, the small cart recoils at 0.870 m/s . What is the speed of the large cart after the collision? Express your answer to three significant figures and include the appropriate units.

Answer 1

The speed of the large cart after the collision is 0.0248 m/s.

Step-by-step explanation:

In this example we will use the Conservation of Momentum.

The Conservation of Momentum states that the momentum of a system is remains the same if no external forces are acting on the system.

Our question is an example of a partially elastic collision.

In a partially elastic collision momentum is conserved and the 2 objects move at different speeds. Kinetic energy is not conserved.

We can come up with an equation for this situation

`m_1V_(i1) +m_2V_(i2)=m_1V_(f1) +m_2V_(f2)`

Let the small cart be object 1 and let the large cart be object 2.

Convert 300 grams to kilograms.

1 kg = 1000 g

0.3 kg = 300 g

We are given

`m_1=` 0.3 kg

`V_(i1) =` 1.20 m/s

`m_2=` 4.00 kg

`V_(i2) =` 0 m/s

`V_(f1) =` 0.870 m/s

Inserting our values into the equation gives us

`(0.3*1.2)+(4*0)=(0.3*0.870)+(4*V_(f2))`

Lets simplify and evaluate
`V_(f2)`.

Anything multiplied by 0 is equal to 0

`(0.3*1.2)=(0.3*0.870)+(4*V_(f2))`

Evaluate each set of parenthesis.

`0.36=0.261+4V_(f2)`

Subtract
`0.261` from both sides of the equation.

`0.099=4V_(f2)`

Divide each side of the equation by 4.

`0.02475=V_(f2)`

Round to 3 significant figures.

`V_(f2) =0.0248`