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PHYSICS 231 Lecture 14: revision. Remco Zegers Walk-in hour: Monday 9:15-10:15 am Helproom BPS 1248. Chapter 4: Newton’s Laws.

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physics 231 lecture 14 revision

PHYSICS 231Lecture 14: revision

Remco Zegers

Walk-in hour: Monday 9:15-10:15 am

Helproom BPS 1248

PHY 231


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

PHY 231

important equations
Important equations

Newton’s second law: F=ma

Gravitational Force: F=mg F=Gm1m2/r2

Earth: m1=mearth


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


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)

PHY 231

example 1
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?

PHY 231

example 2
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.

PHY 231

example 3
example 3
  • A 1000-kg car is pulling a 300 kg trailer. Their acceleration
  • is 2.15 m/s2. Ignoring friction, find:
  • the net force on the car
  • the net force on the trailer
  • the net force exerted by the trailer on the car
  • the resultant force exerted by the car on the road

PHY 231

example 4

1 kg

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

0.5 kg?



2 kg

PHY 231

example 5
example 5

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?


PHY 231

example 6
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

PHY 231


Revision: chapter 5

  • Work: W=Fcos()x Energy transfer
  • Power: P=W/t Rate of energy transfer
  • Potential energy (PE) 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


  • 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 (KEi+PEi)-(KEf+PEf)=Wnc

PHY 231

example 7
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

PHY 231

example 8
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?

PHY 231

example 9
example 9

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.



PHY 231


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?

PHY 231

example 11
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)?
  • 10/8
  • 8/10
  • 1
  • 10/5
  • 8/5
  • 100/64

PHY 231

example 12
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.

PHY 231