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 listed

2) True

3) The energy that an object has stored due to its position or shape is called potential energy

4) The potential energy of the block is 490 J

5) The potential energy of the elevator is 750,000 J

Explanation:

1)

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

$E=KE+PE$

Where

KE is the energy due to the motion of the object

PE is the energy due to the position of the object (it can be either gravitational potential energy or elastic potential energy)

In absence of non-conservative forces, such as friction or air resistance, the mechanical energy is always conserved. Therefore, the mechanical energy is conserved in all the situations listed here:

Child on a swing  --> there is a continuous conversion between gravitational potential energy and kinetic energy

Pendulum  --> there is a continuous conversion between gravitational potential energy and kinetic energy

Bow and Arrow  --> there is a conversion between elastic potential energy of the bow and kinetic energy of the  arrow

Roller Coaster --> there is a continuous conversion between gravitational potential energy and kinetic energy

2)

The potential energy of an object is given by

$PE=mgh$

where

m is its mass

g is the acceleration due to gravity

h is the height of the object relative to the ground

While the kinetic energy is given by

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

where

v is the speed of the object

As an object falls to the ground, its height h decreases, therefore the potential energy PE decreases as well. However, the speed of the object, v, increases during the fall, and therefore the kinetic energy KE increases. This means that potential energy is converted into kinetic energy.

3)

Potential energy is the energy possessed by an object due to its position. It can be of two types:

• Gravitational potential energy: it is the potential energy due to the position of an object in a gravitational field. It is calculated as $mgh$, as shown in part 2)
• Elastic potential energy: it is the potential energy stored in an elastic object when it is stretched or compressed. It is calculated as $\frac{1}{2}kx^2$, where k is the spring constant of the elastic object and x is the stretching/compression of the object relative to its equilibrium position.

4)

The potential energy stored in an object held above the ground is given by

$PE=mgh$

where

m is the mass of the object

g is the acceleration of gravity

h is the height of the object relative to the ground

For the object in this problem, we have

m = 10 kg

$g=9.8 m/s^2$

h = 5 m

Substituting, we find

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

5)

As before, the potential energy of the elevator is given by

$PE=mgh$

where m is its mass and h is its height above the ground.

Here we don't have the mass of the elevator. However, we know its weight:

$W=1500 N$

But we also know that the weight of an object is equal to the product between its mass and the acceleration of gravity:

$W=mg$

So we can rewrite the potential energy as

$PE=Wh$

and the height of the elevator is

h = 500 m

Therefore, its potential energy is

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

Learn more about potential energy:

brainly.com/question/1198647

brainly.com/question/10770261

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