# Calculating Mechanical Energy

#### pamelapepper2019

Hi Everyone,

1. The problem statement, all variables and given/known data
A ball was launched upwards and vertically at a speed 3 m/second up to a height 4m. Calculate the mechanical energy of the ball if its weight is 5 Newtons and has a mass 0.5kg .

2. Relevant equations
potential energy= mass x gravitational acceleration x height
kinetic energy= 1/2 mass x velocity x velocity
mechanical energy= potential energy + kinetic energy

3. The attempt at a solution
mechanical energy = potential energy at maximum height
maximum potential energy =mass x gravitational acceleration x maximum height
= 0.5 x 10 x 4
= 20 joules
So, mechanical energy equals 20 joules?

Does this question seem right to everyone? I feel like there is a problem in the question itself. Does anybody else feel the same?

Many thanks,
Pamela Pepper

#### Woody

Perhaps you were surprised by the numerical size of the solution,
(perhaps expecting kilo-joules or similar magnitudes).

If we consider the definition of a Joule: <wikipedia:joule>
Then one Joule is equal to the energy transferred to (or work done on) an object when a force of one Newton acts on that object in the direction of its motion through a distance of one metre.

If we give the object a mass of 1Kg then 1 Newton will accelerate it at 1 m/s/s.
from S=ut+1/2at^2 we can get the time taken for the object to travel 1 metre (accelerating at 1m/s/s from zero).
2=t^2 thus t=1.4142...

In other words 1 Joule will accelerate 1 Kg at 1m/s/s over a distance of 1 metre in just under one and a half seconds.

Looking at this analysis of the magnitude of a joule (with respect to our more familiar units) will hopefully reassure you that 20 joules is not an unreasonable solution.

#### oz93666

"A ball was launched upwards and vertically at a speed 3 m/second up to a height 4m."

So the ball was launched upwards and has a velocity 3m /sec at a height of 4m.

From search "Mechanical energy is the sum of kinetic and potential energy in an object that is used to do work. In other words, it is energy in an object due to its motion or position, or both."

so the mechanical energy is 20 + (0.25 x 9) = 22.25 J

#### Pmb

PHF Hall of Fame
Hi Everyone,

1. The problem statement, all variables and given/known data
A ball was launched upwards and vertically at a speed 3 m/second up to a height 4m. Calculate the mechanical energy of the ball if its weight is 5 Newtons and has a mass 0.5kg .

2. Relevant equations
potential energy= mass x gravitational acceleration x height
kinetic energy= 1/2 mass x velocity x velocity
mechanical energy= potential energy + kinetic energy

3. The attempt at a solution
mechanical energy = potential energy at maximum height
maximum potential energy =mass x gravitational acceleration x maximum height
= 0.5 x 10 x 4
= 20 joules
So, mechanical energy equals 20 joules?

Does this question seem right to everyone? I feel like there is a problem in the question itself. Does anybody else feel the same?

Many thanks,
Pamela Pepper
You can calculate the total mechanical energy at any height since its a constant.

So you seem to have it right.