# Change in momentum, impulse force calculations

In summary, to find the maximum force exerted by the floor on the ball, one must take into account that momentum is a vector quantity and consider the change in direction at the bounce. By doing so, the correct answer of 443N can be obtained.

## Homework Statement

A 178.0g ball is dropped from a height of 2.99m, bounces on a hard floor, and rebounds to a height of 1.36m. The impulse received from the floor is shown below.

(Is a picture of a graph, Y-axis is force, X-axis is time. No numbers are labelled and is simply a line starting at 0 and goes to a peak and back down to zero like a triangle)

What maximum force does the floor exert on the ball if it is exerted for 2.00ms

## Homework Equations

Impulse = Change in Momentum

Momentum = mv
Ui = mgy
KE = 1/2 mv^2

## The Attempt at a Solution

[/B]
Ui = mgy
=5.2157
1/2 mv^2 = 5.2157
v=7.655m/s

(to find velocity just as ball hits the ground)

Pi = (0.178)(7.655)
=1.3626

(Initial Momentum)

Finding velocity just as it bounces back from floor
Uf = KEi
v=5.1629m/s

Pf = 0.919

(final momentum)

Change in momentum = 0.433

DeltaP(change in momentum) = 1/2 Fmax (0.002)

Fmax = 443N (not correct answer) where did I go wrong?

Momentum is a vector quantity. You haven't taken into account the change in direction at the bounce.

Did you take into account that momentum is a vector quantity, so it has direction? How does the final direction of momentum compare to the initial direction of momentum?

[EDIT: oops, my post is redundant to gneill's.]

gneill said:
Momentum is a vector quantity. You haven't taken into account the change in direction at the bounce.

Ouch, thanks a lot that negative sign fixed things up!

DeltaP =2.2816 got me the right answer!

TSny said:
Did you take into account that momentum is a vector quantity, so it has direction? How does the final direction of momentum compare to the initial direction of momentum?
Yeah that fixed things up :)

## What is momentum?

Momentum is a measure of the motion of an object and is calculated by multiplying an object's mass by its velocity.

## What is the principle of conservation of momentum?

The principle of conservation of momentum states that the total momentum of a closed system remains constant, meaning that the initial momentum of the system must equal the final momentum.

## How is change in momentum calculated?

Change in momentum is calculated by subtracting the initial momentum from the final momentum. It can also be calculated by multiplying the force applied to an object by the time it is applied.

## What is impulse force?

Impulse force is the product of the average force applied to an object and the time interval during which it is applied. It is equal to the change in momentum of the object.

## Why are calculations involving momentum and impulse important in physics?

Calculations involving momentum and impulse are important in physics because they help us understand and predict the motion of objects. They also help us analyze and design systems, such as collisions, in a variety of fields including engineering and sports.

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