1. Gravitation

2. Universal Gravitation
Two objects of masses M and m (kg), whose centres are a distance r (m) apart experience a force of attraction:
G = 6.67 x Nm2/kg2
Ex. Force of attaction between you the person you are sitting next to
Pg #22, 28

3. 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?

4. 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) km above the surface of Earth

5. Near Earth Approximation
Close to the Earth the field strength, g, is almost constant
Pg #24, 26, 27

6. On or near the surface of Earth, g is 9. 80 m/s2
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 m/s2 ? At what height above the surface of Earth does this occur?

7. Apparent Weight

8. Apparent Weight
is the contact force exerted on an accelerating object in/against the direction of gravity.

9. Ex. 1: A 500 g mass is hung from a force sensor (Newton scale)
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.

10. a) The elevator is at rest.
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.

11. Dynamics Problems: Pulleys and the Normal Force

12. 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
3 kg
4 kg
2 kg
2.5 kg

13. 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?
Pg. 183 #41
Pg. 165 #1
Pg. 183 #36, 39

14. Determine the normal force and the acceleration of the following:
(Friction is negligible)
40 N
12 kg
40º

15. Friction

16. 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

17. 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
Pg. 183 #41, 42, 48

18. 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
Coefficient of Kinetic Friction

20. 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?

21. A sled of mass 26 kg has an 18 kg child on it
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 = Calculate:
a) the normal force FBD:
b) the force of friction.
c) the acceleration of the sled and child.