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PHYSICS 231
Lecture 14: revision
Remco Zegers
Walk-in hour: Monday 9:15-10:15 am
Helproom BPS 1248
PHY 231
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Chapter 4: Newton’s Laws
 First Law: If the net force exerted on an object
is zero the object continues in its original state of
motion; if it was at rest, it remains at rest. If it
was moving with a certain velocity, it will keep on
moving with the same velocity.
 Second Law: The acceleration of an object is
proportional to the net force acting on it, and
inversely proportional to its mass: F=ma
 If two objects interact, the force exerted by the
first object on the second is equal but opposite in
direction to the force exerted by the second
object on the first: F12=-F21
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Important equations
Newton’s second law: F=ma
Gravitational Force: F=mg
F=Gm1m2/r2
Earth: m1=mearth
r=rearth
g=Gm2/r2=9.8 m/s2
Equilibrium: Fx=0 Fy=0 (object not moving)
FL=0 F//=0
normal force: force perpendicular to surface the object
is resting on, and balancing the component of
the gravitational force perpendicular to the
surface
friction:
F=sn
(s: coef. of static friction)
F=kn
(k: coef. of kinetic friction) s>k
Hooke’s law: Fs=-kx
(k: spring constant)
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example 1
To lift a patient, 4 nurses grip the sheet on which the patient
is lying and lift upward. If each nurse exerts an upward
force of 240 N and the patient has an upward acceleration
of 0.504 m/s2 what is the weight of the patient?
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example 2
A 5.0 kg bucket of water is raised from a well by a rope.
If the upward acceleration of the bucket is 3.0 m/s2, find
the force exerted by the rope on the bucket.
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example 3
A 1000-kg car is pulling a 300 kg trailer. Their acceleration
is 2.15 m/s2. Ignoring friction, find:
a) the net force on the car
b) the net force on the trailer
c) the net force exerted by the trailer on the car
d) the resultant force exerted by the car on the road
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1 kg
A
q=20o
example 4
Is there a value for the static
friction of surface A for which
these masses do not slide?
If so, what is it?
And what if the 2-kg mass is only
2 kg 0.5 kg?
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example 5
F
A force F (10N) is exerted on
the red block (1 kg). The coef.
of kinetic friction between the
red block and the blue one is 0.2.
If the blue block (10kg)rests on a
frictionless surface, what will
be its acceleration?
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example 6
A rocket is fired from a launching pad. The velocity AND
acceleration of the rocket increase with time even though
the thrust of the engine is constant. Why?
a)The gravitational force becomes smaller because the mass
of the rocket becomes smaller (losing fuel)
b) The gravitational constant g becomes smaller if the rocket
travels away from the earth
c) While traveling away from earth, the gravitational pull
from other planets/sun becomes stronger supporting the
further acceleration
d) Because the density of air becomes small, the friction
becomes less
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Revision: chapter 5
 Work: W=Fcos()x
 Power: P=W/t
 Potential energy (PE)






Energy transfer
Rate of energy transfer
Energy associated with
position.
Gravitational PE: mgh
Energy associated with
position in grav. field.
PE stored in a spring: 1/2kx2 x is the compression of the spring
k is the spring constant
Kinetic energy KE: 1/2mv2 Energy associated with
motion
Conservative force:
Work done does not depend on path
Non-conservative force:
Work done does depend on path
Mechanical energy ME:
ME=KE+PE
 Conserved if only conservative forces are present
KEi+PEi=KEf+PEf
 Not conserved in the presence of non-conservative forces
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(KEi+PEi)-(KEf+PEf)=Wnc PHY 231
example 7
m=1 kg
A pendulum is pushed with initial
velocity 0.1 m/s from a height of
1 cm. How far does it compress the
spring? (assume m does not rise
significantly after hitting the spring)
1 cm
k=100 N/m
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example 8
A ‘smart’ student decides to save energy by connecting his
exercise treadmill to his laptop battery. If it takes
70 J to move the belt on the treadmill by 1 meter and
50% of the generated energy is stored in the battery, how
‘far’ must the student run to use his 100 W laptop for free
for 2 hours?
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example 9
h
450
A block of 1 kg is pushed up a 45o
slope with an initial velocity of 10 m/s.
How high does the block go if:
a) there is no friction
b) if the coefficient of kinetic friction
is 0.5.
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example 10
A crate of 50kg is starting to slide from a slope. When it
reaches the bottom, it is caught by a spring with a spring
constant of 1000 N/m. a) If the crate was originally at a height
of 10 m and friction can be ignored, how much is the spring
maximally compressed?
b) if the frictional force is 100N and
the length of the slope is 15m, what is
the maximal compression?
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example 11
A car (A) can accelerate from 0 to 10 m/s in 5 s. Another
car (B) of the same mass as A can reach 8 m/s in 5 s seconds.
What is the ratio of the power of car A to car B ( PA/PB)?
A)
B)
C)
D)
E)
F)
10/8
8/10
1
10/5
8/5
100/64
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example 12
A 70-kg diver steps of a 10-m tower and drops, from rest
straight down into the water. If he comes to rest 5.0 m
below the water surface, determine the average resistive
force exerted by the water.
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