Gravitation
Universal Gravitation

Two objects of masses M and m (kg),
whose centres are a distance r (m) apart
experience a force of attraction:
GMm
Fg  2
r

G = 6.67 x 10-11 Nm2/kg2

Ex. Force of attaction between you the person you are
sitting next to.

Two tankers of equal mass attract each other with a
force of 3.5 x10-3 N. If their centres are 85 m apart, what
is the mass of each tanker?

For this problem, use ratios only to obtain the weight of
a person at the following distances. Assume the person
weighs 980 N on the surface of Earth. Earth’s radius is
6.38 x 106 m.
a) Three times the distance from the centre of Earth
b) 128 000 km above the surface of Earth
Near Earth Approximation

Close to the Earth the field strength, g, is
almost constant
GM
g 2
r
Fg  mg

On or near the surface of Earth, g is 9.80 m/s2. At what distance
from Earth’s centre is the value of g 9.70 m/s2 ? At what height
above the surface of Earth does this occur?
Apparent Weight
Apparent Weight

is the contact force exerted on an
accelerating object in/against the
direction of gravity.

Ex. 1: A 500 g mass is hung from a force
sensor (Newton scale). What is the
tension, the reading on the scale, under
the following cases?
 a)
the mass was at rest
 b) the mass was moving up with a constant speed.
 c) the mass was moving and accelerating upwards.
 d) the mass was moving down with a constant speed.
 e) the mass was moving and accelerating in a
downward direction.

Pg 165 # 1. If you were standing on a bathroom scale in
an elevator, the normal force acting on you would be the
reading on the bathroom scale. This number is called
your apparent weight. For the following cases, use FBDs
and Fnet statements to calculate the reading on the
bathroom scale (the force normal, FN).
The mass of the person is 70 kg.
a) The elevator is at rest.
b) The elevator is moving up at a constant speed of 10 km/h.
c) The elevator is moving down with an acceleration of 2.0 m/s2.
d) The elevator is moving up with an acceleration of 3.0 m/s2.
e) The elevator cable broke and the elevator is free-falling.
Dynamics Problems:
Pulleys and the
Normal Force
Pulleys

A pulley is a simple machine that changes
the direction of a force

Ex. Find the acceleration of the masses and tension in the ropes
2 kg
3 kg
4 kg
2.5 kg
Normal Force

The normal force (FN) is a reaction force.
If an object pushes onto a surface the
normal force is the reaction force of the
surface pushing back.

Ex. A 20 g fridge magnet is being held onto the fridge by
a 0.9 N force. What is the normal force?

Determine the normal force and the
acceleration of the following:
(Friction is negligible)
40º
40 N
12 kg
12 kg
40 N
Friction
Friction

Friction is the force that stops two surfaces
from sliding across each other

It depends on:
 The
two surfaces
 The force pressing them together
Static vs. Kinetic

Static Friction (SFN): The maximum force
that stops an object from moving
Fs = SFN

Kinetic Friction (kFN): The minimum force
necessary to keep something moving
Fk = kFN
Coefficients of friction, μ

The coefficient of friction is the ratio of the magnitude of
the force of friction to the magnitude of the normal
force.

The value for the coefficient of friction depends on the
nature of the two surfaces in contact and the type of
friction—static or kinetic.
Coefficient of Static Friction
Fs
s 
FN
Coefficient of Kinetic Friction
Fk
k 
FN

Ex 1.

What is the minimum force needed to move a 2000 kg car on
asphalt from rest?

What is the acceleration of the car if the same force was
continuing to apply to the car?

A sled of mass 26 kg has an 18 kg child on it. The big
brother is pulling with a force 30 N to the right and 10 N
up; and the big sister is pushing at 40 N right and 16 N
down. Given μk = 0.12. Calculate:
a) the normal force.
FBD:
b) the force of friction.
c) the acceleration of the sled and child.