Question

A pear hangs in a tree at a height of 1.8 m. The pear has a mass of 0.2 kg. The pear falls out of the tree and lands on the ground. (Use correct units in all answers.)

a. How much gravitational potential energy does the pear have before it falls?

b. How much kinetic energy does it have when it reaches the ground?

c. How fast is the pear moving when it hits the ground?

Answer 1

Potential Energy at the top = 3.528 J

Kinetic Energy when reaching the ground = 3.528 J

Speed when hitting the ground: 5.94
`(m)/(s)`

Step-by-step explanation:

a) recall the formula for the potential gravitational energy: m*g*h

(mass times the acceleration of gravity times the height at which the object is located relative to ground)

In this case the mass is 0.2 kg, the Height is 1.8 m and gravity is 9.8 m/s^2. All these in Si units, so their product will also give SI units: Joules.

`Potential\,Energy= m*g*h\\Potential\,Energy=0.2*9.8*1.8 \,J\\Potential\,Energy=3.528\,J`

b) As the pear reaches the ground, its Potential Energy has been converted in Kinetic Energy, therefore the pear's Kinetic Energy at reaching the ground is also: 3.528 J

c) To find the pear's speed we use the Kinetic Energy formula:

`KE=(1)/(2) m\,v^2`

where v represents the pear's speed. We replace the appropriate values for our case: KE = 3.528 J, mass = 0.2 kg, and solve for the speed:

`KE=(1)/(2) m\,v^2\\3.528\,J=(1)/(2) \,0.2\,kg\,v^2\\3.528\,J=0.1\,kg\,v^2\\v^2=(3.528\,J)/(0.1\,kg) \\v^2=35.28\,(J)/(kg)\\v=√(35.28)\, (m)/(s) \\v=5.94\,(m)/(s)`