Gravitation

Universal Law of Gravitation

• Every mass attracts every mass in universe - Fg.

• Fg directly proportional to mass.– Doubling the mass of one object doubles the force of

gravity between the two objects.

• Fg decreases with the square of the distance between their centers.

– Doubling distance between two objects weakens force of gravity by a factor of 22 (or 4).

NEWTON’S UNIVERSALLAW OF GRAVITATION

Fg =GM1m2

r2

• G universal constant = 6.67 x 10-11 N m2. kg2.

• M1 m2 are mass of objects - kg.

• r is distance between ctrs m.• When standing on planet surface, r = planet radius.

Make a sketch graph of Fg (Y axis) vs. distance (X axis). As 2 objects get further apart, what happens to Fg?

Fg

D between objects

• For any two particular masses, the gravitational force between them depends on their separation as:

distance between the masses increasing

magnitude of the

gravitational force

between 2 fixed

masses

as the separation between the masses is increased, the gravitational force of attractionbetween them decreases quickly.

Gravity and Weight

• The weight of an object is a measure of the gravitational force the object feels in the presence of another mass.

• If one mass is large we s/t call it M and the small mass m.

Ex 1: Write the equation we use to calculate weight on Earth.

• Fg = mg.

Calculate the weight of 1-kg object on Earth.

Calculate gravitational attraction between the Earth & the same 1-kg object. Use your tables to find Earth’s mass & radius.

Solution

• Fg = GMm/r2.

• Fg = (6.67 x 10-11)(5.98x1024kg)(1kg) (6.37 x 106m)2.

• 9.8 N

• THE SAME VALUE!

2. Use the Universal Law of Gravity to find the weight of a 50-kg person in Newtons on Earth?

3. What would be the weight of the 50-kg person on a planet whose radius is 3 x 106 m.and whose mass is 6 x 1022 kg?

4. What is g, the accl of gravity on that planet?

For a 50 kg person:

W= Fg = mg

(50 kg) (~10 m/s2) = 500 N.

For a 50 kg person on the new planet:

W = mg = GMm.r2.

(6.67x10-11)(6 x 1022 kg)(50kg). (3 x 106 m)2

W = 22.2 N

4. Find the distance between a 0.3 kg ball and a 0.4 kg ball if the gravitational force between them is 8.92 x 10-11 N.

• 0.3 m

Trick for finding F if a variable is doubled, halved etc.

• Write the equation out.

• Replace any variable that is not changing with the number 1 (as a place holder).

• Replace any variable that is doubled with the number 2, any that is halved with the number ½, etc.

• Solve the equation with the replacements.

• Your answer is the factor by which to multiply F.

• Ex: if your answer is 3, then F is tripled, if it is ¼ then it is quartered…etc.

5. What happens to Fg between 2 masses A & B if:

• Mass A is tripled?• Mass A is doubled and mass B is

halved?• The distance between their centers is

doubled?• Mass A is tripled and the distance

between their centers is tripled?

Hwk textbook:Read 263 – 265do pg 265: prac prb’s 2,3

Film Clips

• Mech Universe apple and moon• .

http://www.youtube.com/watch?v=JCh9uXy8PHI Isaac Newton 15 min.

Concept Check 1: How does a person’s weight differ at 100 km above the Earth’s surface compared with at the surface?

• 1. The weight is always less than their weight at the surface.

• 2. Their weight is more than their weight at the surface.

• 3. Their weight is the same as at the surface.

Gravitational Field: A region of space where mass feels Fg toward center of planet or star.

Each point has a certain degree of pull.

Gravitational Field Vectors

• A region of space where mass feels gravitational force.• g the gravitational field measured in N/kg.• It is how hard (N) gravity pulls on each kg of mass

affected by it.

• Gravitational field strength (g) • Same as accl of grav.• g = GM/r2.• g = Fg/m

Gravitational Field

Ex 1. What is the gravitational field strength at a point where a 10-kg mass has a weight of 25-N?

• Field strength is the same as accl grav!

• g = Fg

m.

• 25-N/10-kg• g = 2.5 N/kg.

2. Calculate the gravitational field strength at a point 9,000 km above the Earth’s surface.

• Find r. • 6.37 x 106 m + 9000 x 103 m• 1.537 x 107 m• g = GM/r2.• (6.67 x 10-11)(5.98x1024) / (1.537 x 107 m)2.• 1.69 N/kg.

3. An 50-kg object weighs 22.2 N at a point above the Earth. What is the gravitational field strength at that point?

Fg = mg g = Fg/m

= 22.2 N = 0.44 N/kg. 50 kg

Ex 4. A 60-kg student has a weight of 50-N on planet X. What is the gravitational field strength on planet X?

• g = Fnet

m• g = 50-N

60-kg

• g = 0.83 N/kg.

Grav Einstein

• http://www.youtube.com/watch?v=4yyb_RNJWUM

HWK Rb pg 105 #32-38