Mechanical EnergyChapter 16/17

Kinds of Energy

• Gravitational Potential Energy: due to position• Kinetic Energy: due to motion• Heat Energy: due to movement of heat energy

from regions of high energy to areas of low energy.

• Radiant Energy: due to light• Chemical Potential Energy: due to bonds• Elastic Energy: stressed objects that return to

their original shape.• Electrical Energy: due to movement of electrons• Nuclear Energy: due to atomic fission/fusion

Kinetic Energy

• Kinetic Energy is the energy an object has due to its motion.

• Kinetic energy is the energy of a moving object.

• The KE depends on the mass and the speed.

• Ek, KE= ½ mv2, unit is Joule, J

• m is mass in kg, v is velocity in m/s

Activity

• What is the KE of a 6 kg curling stone moving at 4 m/s?

• KE = ½ mv2

• = ½ x 6kg x (4 m/s)2

• = ½ x 6 x 16• = 48 J

• Do page 341, Q. 1- 4

Exam QuestionThe kinetic energy of an object depends on several factors. Which one of the following graphs represents the change in kinetic energy of an object as a function of its speed? A)

Kineticenergy

Speed0

C) Kineticenergy

Speed0

B) Kineticenergy

Speed0

D) Kineticenergy

Speed0

Exam Question

An car, travelling along a horizontal road, has kinetic energy of 1.6 106J. The driver slows the car to half of its original speed. What is the new kinetic energy of the car?

A)

1.6 106 J

B)

8.0 105 J

C)

4.0 105 J

D)

1.6 105 J

Activity

• Page 341, Q 1 - 6

Potential Energy• If we put work into an object (W=FΔd) by

lifting it up against gravity, it now has the ability to move; it has the potential to fall down and use up the energy we put into it.

• W = FΔd = mgd

• Ep , PE = mgh, unit is Joules, J

• m is the mass in kg

• g is the acceleration due to gravity

• h is the height above the Earth’s surface, m.

Activity

• What is the PE of a 10 kg weight, 8 m above the ground?

• PE = mgh = 10 kg x 9.81m/s2 x 8m

• = 784.8 J

• Page 349, Q. 1-4

Exam QuestionA weather balloon with a mass of 4.0 kg, including the weather instruments, rises vertically in the air. It passes an altitude of 200 metres at a velocity of 2.0 m/s.

2.0 m/s

200 m

At this point what is its potential energy with respect to the ground? A)

8.0 103 J

B)

8.0 102 J

C)

8.0 101 J

D)

8.0 J

Total Energy

• The energy of a system transfers between Potential Energy and Kinetic Energy.

• Total Energy = PE + KE• The PE of an object getstransferred to KE as itspeeds up. • As the PE decreases, theKE increases.

Total Energy• What is the speed of a 500g rock that

drops from a height of 78.4 m, just before it hits the ground?

• ET = KE + PE, at first, v = 0 m/s

• = ½ mv2 + mgh, since v = 0, KE = 0

• = 0.5kgx9.81m/s2x78.4m, ET = PE only

• = 384.6 J

• As the rock approaches the ground all its PE is transferred to KE, so PE = 0. So…

Total Energy, Part Deux

• ET = PE + KE

• 384.6 J = KE

• 384.6 = ½ mv2

• 384.6 = 1/2x 0.5kg x v2

• 1538.4 J = v2

• v = 39.2 m/s

• So just before it hits the ground, the rock has a speed of 39.2 m/s

Another way to solve it

• Same situation, just look at the speed and distance.

• We could use v2 = u2 + 2as• = 02 + 2(9.81)(78.4)• = 1538• So, v = 39.2 m/s• Both methods work, depending on the

information given. • Page 353, Q. 2-5• Page 356, Q. 6

Exam QuestionA small airplane with a mass of 1000 kg, is flying at 60 m/s at an altitude of 250 m.

250 m

60 m/s

What is the total mechanical energy of this airplane with respect to the ground?

A)

1.8 106 J

B)

2.5 106 J

C)

4.3 106 J

D)

6.1 106 J

Exam QuestionA go lf ball is d ropped ou t o f a w indow w h ich is 10 m above the ground . T he ball has a m ass o f 50 g . D isregard the effects o f a ir resistan ce.

10 m

W hat is the k inetic energy o f the b all ju st befo re it h its the ground?

A )

10 J

B )

7 .5 J

C )

5 .0 J

D )

2 .5 J

Exam QuestionA s to n e w i th a m a s s o f 1 0 0 g i s th r o w n h o r iz o n ta l l y f r o m th e to p o f a c l i f f o v e r lo o k in g th e o c e a n w i th a v e lo c i t y o f 2 0 m /s . D is r e g a r d th e e f f e c t s o f a i r r e s i s t a n c e .

1 5 m

2 0 m /s

W h a t i s th e k in e t i c e n e r g y o f th e s to n e ju s t b e f o r e i t h i t s th e w a te r ?

A )

1 5 J

B )

2 0 J

C )

3 0 J

D )

3 5 J

Exam Question

A 100 g ball is thrown vertically upward from the ground with a velocity of 20 m/s. Disregard the effects of air resistance. What is the kinetic energy of this ball after it has risen 5.0 metres?

A) 20 J

B)

15 J

C)

10 J

D)

5.0 J

Summary

• Energy is the ability to do work.• Work is the transfer of energy. (W=ΔE)• Friction often does negative work on an

object because it removes energy from it.• Gravitational Potential Energy is the

energy of an object due to its height above the Earth’s surface. PE = mgh

• Kinetic Energy is the energy of a moving object. KE = ½ mv2

Summary

• The Law of Conservation of Energy states that in any transfer or transformation of energy, the total amount of energy remains the same.

• The form of the energy may be changed, e.g. noise, heat, vibration, friction.

• In situations where friction and air resistance are small enough to be ignored, and where no other energy is added to the system, the total mechanical energy is conserved.

Summary

• E total = KE + PE (before) = KE + PE (after)

• Heat is the measure of the amount of thermal energy that flows from one body to another because of a difference in temperature.

• Work done on an object can cause an increase in the temperature of an object.

Exam Question

The starter motor of a car is not working. One person stays in the car while the other pushes it from behind to get it up to a certain speed so that it can be started. The car and the person inside it have a total mass of 1.00 103 kg. Disregard the effects of friction. The car is at a complete stop. The person who pushes it exerts a force of 2.00 102 newtons for 15.0 seconds. How much kinetic energy does the car gain as a result of the push?

A)

1.80 104 J

B)

1.35 104 J

C)

9.00 103 J

D)

4.50 103 J

Activity

• Page 361, Q. 1-7

Elastic Potential Energy

• We know Hooke’s Law – F = kx– k – spring constant, N/m– x – elongation of the spring, m

• The energy stored in a spring.

• E PE = ½ k (x)2

Activity

• The length of a compressed spring, unextended, is compressed by 5 cm, using a force of 20 N. Calculate the energy stored in the spring.

• Using F = kx

• 20 = k (0.05 m)

• k = 400 N/m

Continued

• E PE = ½ k (x)2

• = ½ (400) (0.05) 2

• = 0.5 J

• Do Page 373, Q 1-3.