Energy

One exciting thing from energy is the gliding through the air on a mountain bike or in a wingsuit.


glide

Quantities in Energy

Name Symbol Unit Type
Total energy ET, ETOT J, joules scalar
Potential energy, gravitational potential energy PE J, joules scalar
Kinetic energy KE J, joules scalar
Internal energy, Heat energy Q J, Joules scalar
Work W J, joules scalar
Power P W, watts scalar
Force F N, newtons vector
bike

Key Things to Know in Energy

Key Words in Energy

Energy, Mechanical energy, Elastic potential energy, Gravitational energy, kinetic energy, power, work

Formula in Energy

Example 1

A block slides across a rough, horizontal tabletop. As the block comes to rest, there is an increase in the block-tabletop system’s
(1) gravitational potential energy
(2) elastic potential energy
(3) kinetic energy
(4) internal (thermal) energy

h = fixed, PE = mgh = fixed. v = smaller, KE = decrease. Mechanical energy decreases, but the total energy must remain the same. Therefore, the energy is transfered into the heat energy account. The heat energy (internal energy) is increased.

Example 2

A pendulum is made from a 7.50-kilogram mass attached to a rope connected to the ceiling of a gymnasium. The mass is pushed to the side until it is at position A, 1.5 meters higher than its equilibrium position. After it is released from rest at position A, the pendulum moves freely back and forth between positions A and B, as shown in the diagram below.
Q 2 picture
What is the total amount of kinetic energy that the mass has as it swings freely through its equilibrium position? [Neglect friction.]
(1) 11 J (3) 110 J
(2) 94 J (4) 920 J

E = PE + KE = remains fixed. At position A, EA = PE + KE = mgh + 0 = 7.5 kg × 9.8 m/s2 × 1.5 m = 110.25 J. EB = EA. EB = mgh + KE = 0 + KE = KE. KEB = 110.25 J

Example 3

A student produced various elongations of a spring by applying a series of forces to the spring. The graph below represents the relationship between the applied force and the elongation of the spring.
Q 3 picture
a) Determine the spring constant of the spring.
Fs = k x; k = Fs/x = 4 N/0.2 m = 20 N/m


b) Calculate the energy stored in the spring when the elongation is 0.30 meter.
Potential energy stored in the spring PEs = \( \frac{1}{2} \) k x2 = \( \frac{1}{2} \) 20 N/m (0.3 m)2

Example 4

The diagram below represents a 155-newton box on a ramp. Applied force F causes the box to slide from point A to point B.
Q 4 picture
What is the total amount of gravitational potential energy gained by the box?
(1) 28.4 J (3) 868 J
(2) 279 J (4) 2740 J

155 N means the force of gravity on the box Fg = mg = 155 N; PE = mgh = 155 N × 1.8 m = 279 J

Exercises

1. Which statement describes the kinetic energy and total mechanical energy of a block as it is pulled at constant speed up an incline?
(1) Kinetic energy decreases and total mechanical energy increases.
(2) Kinetic energy decreases and total mechanical energy remains the same.
(3) Kinetic energy remains the same and total mechanical energy increases.
(4) Kinetic energy remains the same and total mechanical energy remains the same.

2. Calculate the kinetic energy of a particle with a mass of 3.34 × 10-27 kilogram and a speed of 2.89 × 105 meters per second.

3. A child, starting from rest at the top of a playground slide, reaches a speed of 7.0 meters per second at the bottom of the slide. What is the vertical height of the slide? [Neglect friction.]
(1) 0.71 m (3) 2.5 m
(2) 1.4 m (4) 3.5 m

4. The gravitational potential energy, with respect to Earth, that is possessed by an object is dependent on the object’s
(1) acceleration (3) position
(2) momentum (4) speed

5. A boy pushes his wagon at constant speed along a level sidewalk. The graph below represents the relationship between the horizontal force exerted by the boy and the distance the wagon moves.
exercise Q 5 picture
a) What is the total work done by the boy in pushing the wagon 4.0 meters?
(1) 5.0 J (3) 120 J
(2) 7.5 J (4) 180 J

b) As the boy pushes the wagon, what happens to the wagon’s energy?
(1) Gravitational potential energy increases.
(2) Gravitational potential energy decreases.
(3) Internal energy increases.
(4) Internal energy decreases.