Physics 20 PM GROUP only Week 8 Summative TaskDue May 29th .

Please try to stay in the time constraints from the Weekly Plan. If it is taking you too lone, please contact me. You may skip over some questions if time is an issue,

so you get some of each type done

Universal Law of GravitationGravity is known to be the pull of any objects with mass towards any other objects with mass. We most often look at it as our experience of being pulled towards the earth. We don’t often consider our attraction to the lamp on our desk, the pear in our lunch, the chair we sit on, or a car driving past. Usually this is because the gravity from the massive earth is so strong that all other gravitational forces aren’t noticed.

Things to note, any two objects with mass are attracted by gravity.

No matter what the two objects size or masses are, the gravitational forces are equal (Newton’s third law)

We often use the shortcut when we are on the surface of the earth where gravity is 9.81m/s2. But this only works on the surface of the earth where we can use Fg=mg

The true equation for gravity is called the Universal Law of Gravitation

Gravity is an attractive force only. It is normally very weak, but if you have very large masses like planets, stars, etc it can be strong and act over large distances

Cavendish studied the relationship between distance and force to come up with the equation and solve for the universal gravitational constant G. When solving for radius it is from the center to center of the objects.

ALL FORCE QUESTIONS MUST HAVE A FBD

1. Find the force of gravity (weight) of a 100kg object on the surface of the earth (6.37 x 106m, which has a mass of 5.97x1024kg) using:

a. F=mgb. F=Gmm/r2

2. Find the attraction (of gravity) between Goofy (80kg) and Micky Mouse (65kg) if they are 2.5m apart.

3. Find the force of gravity acting on a 3000kg satellite 45km above the surface of the Earth. (note: above the surface means add the radius of the earth to the height to get the radius)

4. Find the distance between two masses which are, 85kg and 120kg that have a force of attraction of 8.6 x 10-7N

5. What happens to the force of gravity when both masses triple and the radius doubles.

6. Find the force of gravity between the sun and the Earth. You will need to look up values online.

Cavendish experimentally determined the relationship between the force acting on two masses and the radius between them. Using the following experimental results complete the following:

a. graph a Fg vs r graph (5)Radius (cm) Force (x 10-7 N)

10 480

20 120

30 52

40 33

50 19

60 13

70 11

80 7

Kepler’s Laws

Kepler was an astronomer who helped to shape our understanding of how planets moved in our solar system. His model is based on three principles discovered through many years of study and following the motion of the planets.

1st Law:

Planets follow elliptical orbits, not circular. These orbits have 2 foci, one of them is the sun and the other a point in space.

2nd Law:

For equal amounts of time, the area that the planets open up between the sun and the partial circumference are equal. This means the closer to the sun, the faster you go.

3rd Law:

For any bodies with objects in orbit, there is a constant value k based on the relation of time and radius of orbits.

T2

=T2

r3 r3

This third law is very helpful in comparing two satellites orbiting the same celestial body.

Kepler Problem:

1. How much farther is Jupiter than the Earth if a year on Jupiter is 12 years?

Circular Motion and Gravitation (use constants from your data sheet)

(Fc=Fg) or (m4π2r/T2 = Gmm/r2)Problems:

1. Find the mass of Planet Batman if one of her moons orbits every 21day (each day on this planet is the same as a day on Earth), at a radius of 2.55 x 106m

2. What is the radius of the moons orbit around the earth if it takes 27.4 day to complete one orbit

THE FOLLOWING MATERIAL IS FOR WEEK 8, THE PREVIOUS WAS FROM WEEK 7 MATERIAL

Force of Friction causing Centripetal Motion Centripetal force is the NET FORCE acting on an object to keep it moving in a circle. When caused by friction on a flat (not inclined) surface, we typically know the speed of a vehicle, so it leaves us using this equation for Fc.

When we have that equal to the force of friction, manipulate it from scratch, using your FBD to find an equation relating the variables for Fc and Ff

Show all givens, equations, work and units in your problem solving. Be sure to show an Fnet diagram for circular motion.

1. What force of friction is required to keep a 2000kg cruck on a roundabout, with a diameter of 62m, and a speed limit of 30km/h?

2. A 1230kg car is travelling 75km/h around a curve with a coefficient of friction of 0.77. What is the radius required for the car to stay on the road?

3. What is the maximum speed that the Batmobile can go around a corner in Gotham with a radius of 6.7m if the coefficient of friction is 0.62?

4. A roundabout needs a speed limit. It has a radius of 25m. The coefficient of friction depends on the weather:

a. Dry = 0.88b. Rainy = 0.68c. Snowy = 0.55d. Icy = 0.28

Solve for and explain the speed limit you would post on the road.

1. A 750kg car drives around a curve in the road with a radius of 25m. What is the maximum speed they can go if the coefficient of friction is 0.77?

2. You are designing a road with a bend around a hill with a diameter of 125m. What is the necessary coefficient of friction if the speed limit is 90.0km/h?