Question

In which of these situations, is mechanical energy being conserved? (Neglect, air resistance, friction, and breaking) Check all that apply.
Child on a swing


Pendulum


Bow and Arrow


Roller Coaster

Question 2
As an object falls to the ground, its potential energy is being converted to kinetic energy.


True
False
Question 3
The energy that an object has stored due to its position or shape is called:

kinetic energy


potential energy


chemical energy


electrical energy

Question 4
Calculate the potential energy stored in a 10 kg block, 5 meters above the ground.


490 J


50 J


490 N


50 N

Question 5
An elevator weighs 1500 Newtons. Calculate how much potential energy it has when it is lived 500 meters in the air.


75,000 J


750 J


7,500,000 J


750,000 J

Answer 1

1) Mechanical energy is conserved in all the situations mentioned

2) True

3) Potential energy

4) The potential energy is 490 J

5) The potential energy is 750,000 J

Explanation:

1)

The mechanical energy of an object is the sum of its potential energy (PE) and its kinetic energy (KE):

$E=PE+KE$

When there are no conservative forces acting on the object (i.e. air resistance of friction), the mechanical energy is always conserved, so it is constant:

$E=const.$

This means that there is a continuous conversion between potential energy and kinetic energy.

In all the examples mentioned here, there are no air resistance or friction acting on the system: therefore, mechanical energy is conserved in all cases.

2)

The potential energy of the object falling to the ground is given by

$PE=mgh$

where

m is the mass

g is the acceleration of gravity

h is the height of the object above the ground

While the kinetic energy is given by

$KE=\frac{1}{2}mv^2$

where

v is the speed of the object

As the object falls, its height h decreases, while the speed v increases: therefore, the potential energy decreases and it is converted into kinetinc energy, which increases.

3)

The energy possessed by an object due to its position is called potential energy. It can be of two types:

- Gravitational potential energy: it is the energy possessed by an object due to its position in a gravitational field. It is given by

$PE=mgh$

where m is the mass, g the acceleration due to gravity, h the height of the object

- Elastic potential energy: it is the energy stored in an elastic object which is compressed or stretched - it is given by

$PE=\frac{1}{2}kx^2$

where k is the spring constant and x the elongation of the object relative to its equilibrium position.

4)

The (gravitational) potential energy stored in the block is calculated  as

$PE=mgh$

where:

m = 10 kg is the mass of the block

$g=9.8 m/s^2$ is the acceleration due to gravity on Earth's surface

h = 5  m is the height of the object above the ground

Substituting, we find the potential energy:

$PE=(10)(9.8)(5)=490 J$

5)

The potential energy of the elevator is given by

$PE=mgh$

In this case, we have

h = 500 m (height of the elevator)

W = 1500 N (weight of the elevator)

We also know that the weight is the product of mass and acceleration due to gravity:

$W=mg$

So we can rewrite the first equation as

$PE=Wh$

And substituting, we find

$PE=(1500)(500)=750,000 J$

Learn more about potential energy:

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