Download 8.4 Conservation of Energy Part II

Name: ____________________
Physics 11
Date: _______________
Chapters 8, 9 Work and Energy
Lesson 4: Law of Conservation of Energy Part II
Energy is neither created nor destroyed. It may only be transformed from one type to another. This
means that if we are looking at a closed system (a situation that has no outside sources of energy), the
total amount of energy at the start and the total amount of energy at the end must be the same.
As an equation, we write:
Show marble energy transfer device.
When the ball is at the top of its bath, all its energy is __________________________. The ball is not
moving.
As the ball falls, it loses its potential energy and
gains energy of the motion, which called ______________________. The amount of _______
at the bottom of its fall is given by
But at all times the SUM of the gravitational potential energy and the kinetic energy is constant.
The total energy of a mechanical system is constant. Energy may be transformed
from one form into another, but the total amount of energy id unchanged
Look at the ball, as it falls through positions 1, 2 , 3 etc. the sum of the the potential energy and the
kinetic energy remain constant:
And to calculate the velocity of the marble at the bottom of the swing, __________________, and
___________________, but the kinetic energy at the bottom of the swing must equal the gravitational
potential energy at the top ( according to the law of conversation of Mechanical Energy).
THUS,
_________________________________
Therefore, ________________________________
And,
__________________________________
Example 1: a) A projectile is launched straight up into the air. If its initial velocity was 84.3 m/s, how
high does it go? Use energy (ignore air friction).
b) If the projectile only reaches a height of 72 m, how much work did air friction do on the way up?
Example 2: At location Z, a 72 kg skier is travelling at 18 m/s. How high up the next slope can the skier
reach (ignore friction)?
Example 3: A 245 kg roller coaster car travels as shown below. At point A it is moving at 12.0 m/s.
a) If we ignore friction, how fast will it be travelling when it reaches point B?
b) If the coaster is only travelling at 15.0 m/s at point B, how much energy was lost to heat?
Example 4: A 25 kg object is dropped from a height of 42.0 m and lands in the snow with a speed of 25
m/s. How much heat energy was produced during the fall?
Example 5: A toy car with a mass of 212g is pushed by a student along a track so that it is moving at
12m/s. It hits a spring (k = 52.8 N/m) at the end of the track, causing it to compress.
a) Determine how far the spring compressed to bring the car to a stop.
Name: ____________________
Physics 11 H.
Date: _______________
Chapters 8, 9 Work and Energy
Assignment 4: Law of Conservation of Energy Part II
1. A physics student lifts his 2.0 kg pet rock 2.8 m straight up. He then lets it drop to the ground. Use the Law
of Conservation of Mechanical Energy to calculate how fast the rock will be moving (a) half way down and
(b) just before it hits the ground.
2. A 65 kg girl is running with a speed of 2.5 m/s. How much kinetic energy does she have? She grabs on to a
rope that is hanging from the ceiling, and swings from the end of the rope. How high off the ground will she
swing?
3. How much kinetic energy does the 80.0 kg
skier sliding down the frictionless slope in
Figure 6.7 have when he is two-thirds of the
way down the ramp? The vertical height of
the ramp is 60.0 m.
Figure 6.7
4. A golfer wishes to hit his drives further by increasing the kinetic energy of the golf club when it strikes the
ball. Which would have the greater effect on the energy transferred to the ball by the driver  doubling the
mass of the club head or doubling the speed of the club head? Explain.
5. A rubber ball falls from a height of 2.0 m, bounces off the floor and goes back up to a height of 1.6 m. What
percentage of its initial gravitational potential energy has been lost? Where does this energy go? Has the Law
of Conservation of Energy been 'violated'?
6. How much work must be done to increase the speed of a 12 kg bicycle ridden by a 68 kg rider from 8.2 m/s
to 12.7 m/s?
7. A vehicle moving with a speed of 90 km/h (25 m/s) loses its brakes but sees a 'runaway' hill near the
highway. If the driver steers his vehicle into the runaway hill, how far up the hill (vertically) will
the vehicle travel before it comes to a stop? (Ignore friction.) If friction is taken into account, will
the vertical distance the vehicle moves be less or greater than the 'ideal' distance you just solved for,
neglecting friction? Explain.
Figure 6.8
8. A 2.6 kg laboratory cart is given a push and moves with a speed of 2.0 m/s toward a solid barrier, where it is
momentarily brought to rest by its spring bumper. (Figure 6.8) How much elastic potential energy will be
stored in the spring at the moment when the spring is fully compressed? What is the average force exerted
by the spring if it is compressed 0.12 m? (Why is it necessary to specify average force in this situation?)
Answers:
1. (a) 5.2 m/s (b) 7.4 m/s 2. 0.32 m
3. 3.14 x 104 J
4. Ek = 1/2mv , so doubling mass will double kinetic energy, but doubling speed will quadruple kinetic energy.
5. Loss of potential energy = mgho -mgh1 = mg (2.0 m) - mg (1.6 m) = (0.40m) mg
(a loss of 20%) The energy is used to warm the floor and the ball.
6. 3.8 x 103J
7. Without considering friction, 32 m. With friction, the vertical height will be less.
8. 5.2 J
This energy is momentarily stored as spring-potential energy, Ep.
F x = 5.2 J
F = 5.2 J / 0.12 m = 43 N.
The actual force will vary from 0 N to 86 N!
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