Chapter 5, Problem 8TS

A $1-\text{kg}$ ostrich egg is thrown at $2\text{m}/\text{s}$ at a bedsheet and is brought to rest in $0.2\text{s}$. Show that the average amount of force on the egg is $10\text{N}$.

To determine

The average amount of force on the egg.

Answer to Problem 8TS

The average amount of force on the egg is $10\text{N}$.

Explanation of Solution

Given Info: The mass of the ostrich egg is $1\text{kg}$, throwing speed of the ostrich egg is $2\text{m}/\text{s}$, time to ostrich egg come at rest is $0.2\text{s}$.

Write the expression to calculate the momentum of the ostrich egg.

$P=m\cdot v$

Here,

$P$ is the momentum of the ostrich egg

$m$ is the mass of the ostrich egg

$v$ is the throwing speed of the ostrich egg

Write the expression to calculate the impulse on the ostrich egg.

$I=F\cdot t$

Here,

$I$ is the impulse on the ostrich egg

$F$ is the average amount of force on the ostrich egg

$t$ is the time to ostrich egg come at rest

The momentum of the ostrich egg is same as the impulse on the ostrich egg, so equate the above two expressions to calculate the average amount of force on the ostrich egg.

$\begin{array}{c}I=P\\ F\cdot t=m\cdot v\\ F=\frac{m\cdot v}{t}\end{array}$

Substitute $1\text{kg}$ for $m$, $2\text{m}/\text{s}$ for $v$ and $0.2\text{s}$ for $t$ to find $F$.

$\begin{array}{c}F=\frac{\left(1\text{kg}\right)\left(2\text{m}/\text{s}\right)}{0.2\text{s}}\\ =10\text{kg}\cdot \text{m}/{\text{s}}^2\\ =\left(10\text{kg}\cdot \text{m}/{\text{s}}^2\right)\left(\frac{1\text{N}}{1\text{kg}\cdot \text{m}/{\text{s}}^2}\right)\\ =10\text{N}\end{array}$

Conclusion:

Therefore, the average amount of force on the egg is $10\text{N}$.