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Conservation of Energy, the Work-Energy
Theorem, and Projectile Motion
The Mechanical Energy (E) of an object consists of two types of
energy, Potential (U) and Kinetic (K)
E =U + K
For an object at a height H, U = mgH where m is the mass and g is
the acceleration due to gravity (9.81 m/s2). K = ½ mv2 where v is the
speed of the object.
If a non-conservative force e.g. friction, acts on the system, then the
final energy is different from the initial energy and the difference is
equal to the work done by that force (Wnc).
E f − E i = W nc
K f + U f − (K i + U i ) = W nc .
Work done by a force is the scalar product of force and displacement.
Work may be positive,
€ negative, or zero.
W = F • d = Fdcosθ
€
where θ is the angle between the force F and the displacement d .
In the case of work done by friction, θ = 180o, giving W f = − f k d where
f k is the force of friction.
€
€
The work-kinetic energy theorem
states
€
€.
K f = K i − f k d + W other
If the other work is done by gravity, then:
K f = K i − f k d + W gravity
or
€
K f = K i − f k d + mg( H i − H f ).
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Projectile Motion is the special case of two-dimensional motion
experienced by objects only under the influence of gravity. Such
objects, termed projectiles, are under constant acceleration where
ax = 0 m/s2 and ay = - g = -9.81 m/s2.
In this case, the kinematics equations give the results for the
horizontal component of the motion:
v xf = v xi = constant
x f = x i + v xi t
and for the vertical component of the motion:
v yf = v yi − gt
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€
1
y f = y i + v yi t − gt 2
2
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Energy and Projectile Motion 24
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Prelab Questions
These questions need to be completed before entering the lab.
Show all workings.
Attach this sheet to your lab book.
Markers
Initials
Prelab 1
A 500 kg car is at rest at the top of a 50.0 m high hill. Calculate the energy of the
car at the top of the hill.
Prelab 2
The car rolls to the bottom of the hill. At the bottom of the hill, the car has a
speed of 27.8 m/s. Calculate the energy of the car at the bottom of the hill.
(Assume the bottom of the hill has a height of 0 m.)
Prelab 3
Calculate the work done by friction on the car as it rolled down the hill.
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Laboratory #4
Energy and Projectile Motion 25
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Name and Student Number:
___________________________________
Date:
___________________________________
Partner:
___________________________________
Part I :
Introduction
Part II:
Set up
Table 1:
Relative height of track top and bottom. Mass of sliding object.
Value
H
h
m
Part III: Conservation of Energy
QUESTION 1:
Uncertainty
Units
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Laboratory #4
Energy and Projectile Motion 26
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QUESTION 2(a):
2(b):
2(c):
CHECKPOINT:
To be signed after completing Question 2.
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Energy and Projectile Motion 27
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Part IV:
Projectile Motion
Table 2:
Range of mass
Ri (cm)
€
R=
(cm)
σR =
€
N=
(no units)
€
σR =
€
σR
=
N
(cm)
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Energy and Projectile Motion 28
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QUESTION 3:
QUESTION 4:
QUESTION 5:
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QUESTION 6:
QUESTION 7:
Part V:
Summary
QUESTION 8(a):
8(b):
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Energy and Projectile Motion 30
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8(c):
QUESTION 9:
QUESTION 10:
Return to the Lab manual:
Staple sheet with markings
to the reverse of this page.