Question

A lion has a mass of 45 kg. Answer the following questions about it, using correct units. a. The lion runs at a speed of 14.2 m/s. How much kinetic energy does the lion have? (4 points) b. If the lion runs up a hill to a height of 28 m, how much gravitational potential energy has the lion gained? (4 points) c. A fox with mass 1.8 kg is avoiding a lion by climbing into a tree. The fox climbs to a height of 3.8 m and jumps to another tree at a speed of 8.1 m/s. What is the total mechanical energy of the fox as it jumps? (3 points)

Answer 1

A) The kinetic energy of an object is given by:
$K= \frac{1}{2}mv^2$
where m is the mass of the object, and v its speed. For the lion in our problem, m=45 kg and v=14.2 m/s, so its kinetic energy is
$K= \frac{1}{2}mv^2= \frac{1}{2}(45 kg)(14.2 m/s)^2=4537 J$

b) the increase in gravitational potential energy of the lion is given by:
$\Delta U = mg \Delta h$
where g is the gravitational acceleration, and $\Delta h$ is the increase in altitude of the lion. In this problem, $\Delta h=28 m$, so the increase in gravitational potential energy is
$\Delta U=mg \Delta h=(45 kg)(9.81 m/s^2)(28 m)=12361 J$

c) When the fox reaches the top of the tree, its gravitational potential energy is
$U=mgh=(1.8 kg)(9.81 m/s^2)(3.8 m)=67 J$
As it jumps, its kinetic energy is
$K= \frac{1}{2}mv^2= \frac{1}{2}(1.8 kg)(8.1 m/s)^2=59 J$
So the total mechanical energy of the fox as it jumps is
$E=U+K=67 J + 59 J =126 J$