Calculating Impulse in a Collision: Simple Physics 11 Homework Problem

[roxxyroxx]

Homework Statement

A 15.0 g object initially moving to the right at 30.0 cm/s collides with a stationary 45.0 g object. After the collision the 45.0 g object is moving to the right at 15 cm/s.
what impulse does the 45.0 g object apply to the 15.0g object during collision?

Homework Equations

F$$\Delta$$t = m$$\Delta$$v

The Attempt at a Solution

I tried:
F$$\Delta$$t = m$$\Delta$$v
= (15.0g)(15.0cm/s)
= 225 N x s
but the answer is 6.75 x 10^-3 N x s
help ?

 

[Doc Al]

I tried:
F$$\Delta$$t = m$$\Delta$$v
= (15.0g)(15.0cm/s)
= 225 N x s
but the answer is 6.75 x 10^-3 N x s

How did you determine the change in velocity of the 15.0g object?

(Also: Use standard units. Convert g to kg; cm to m.)

 

[thomate1]

Hello,

Thank you for sharing your attempt at solving this problem. I can see that you have correctly identified the equation for calculating impulse, which is FΔt = mΔv. However, there are a few things that need to be addressed in order to arrive at the correct answer.

Firstly, the units for mass should be in kilograms (kg) instead of grams (g). This is because the units for force (F) are in Newtons (N), which is equivalent to kg*m/s^2. So, the equation should be written as FΔt = mΔv, where m is in kilograms.

Secondly, the units for velocity should also be in meters per second (m/s) instead of centimeters per second (cm/s). This is because the units for impulse (FΔt) are in Newton-seconds (N*s), which is equivalent to kg*m/s. So, the equation should be written as FΔt = mΔv, where Δv is in meters per second.

Applying these corrections to your attempt, we get:

FΔt = mΔv
= (0.015 kg)(0.15 m/s)
= 0.00225 N*s
= 2.25 x 10^-3 N*s

This is closer to the given answer of 6.75 x 10^-3 N*s, but it is still not the correct answer. This is because your calculation only considers the change in velocity (Δv) of the 15.0 g object, but it does not take into account the change in velocity of the 45.0 g object. In a collision, both objects experience a change in velocity, so we must consider the total change in momentum (p) of both objects.

Since momentum (p) is equal to mass (m) times velocity (v), we can write the equation as:

p = mv

So, for the 15.0 g object, the change in momentum (Δp) would be:

Δp = mΔv
= (0.015 kg)(0.15 m/s)
= 0.00225 kg*m/s

And for the 45.0 g object, the change in momentum (Δp) would be:

Δp = mΔv
= (0.045 kg)(0.15 m