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## Homework Statement

A fly travelling horizontally in the positive x direction lands on the side of your slice of birthday cake and gets stuck in the icing. Just before striking the cake the fly is travelling at 0.05ms

^{-1}and the fly has a mass of 1 gram.

a) If the collision lasts 10ms, what is the average force on the fly during the collision?

b) What is the average force on the cake?

c) How far is the icing dented, assuming the force during the collision is constant?

## Homework Equations

**FΔt=Δp=Δmv**

**F=ma**

**X**

_{f}=X_{i}+V_{i}t+0.5at^{2}## The Attempt at a Solution

Hey guys :D

I was wondering if my answers are right, it seems correct to me but i'm not too sure...

**A)**

So i just find the change of momentum which is

**Δmv = 0 - (0.001*0.005) = -0.00005kgms**

^{-1}Next, I substitute the change in momentum into the impulse formula and find the force exerted on the fly by the cake

**F = -0.00005/0.01 = -0.005N**

**B)**

From Newton's third law, the average force on the cake exerted by the fly is just the negative of the force on the fly exerted by the cake:

**0.005N**

**C)**

This one i had some trouble, but i pretty sure it's correct...

From the calculated force on the fly from question A, we can use the formula

**F=ma**to determine the acceleration

**a=F/m=-0.005/0.001= -5ms**

^{-2}From this acceleration, we can determine the how far the fly went inside the cake by using the kinematic equation

**X**

_{f}=X_{i}+V_{i}t+0.5at^{2}**X**

_{f}=0+0.05(0.01)-0.5(5)(0.01)^{2}=0.0005-0.00025=0.00025m
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