Unit 06“Circular Motion, Gravitation and Black

Holes”

Test Review

1. What is the centripetal force?

2. What provides the centripetal force in each case below:

A skateboard turning a corner.A person swinging on a swing set.The moon orbiting around the EarthA cart on a rollercoaster.

Answer the following questions:

The force that pulls an object inward, and changes the direction of an object. It causes circular motion.

Friction between the ground and tire.The rope

Gravity

The track

Explain each of the following statements.

1. Mud flies off a tire as the tire quickly turns.

3. Spinning pizza dough will make the pizza dough stretch out and get bigger.

2. When on the “Swings” ride, you move away from the center of the ride as it moves around.

4. You slide to the outside of the car as it turns a corner.

1. Mud flies off a tire as the tire quickly turns.

The tire has an inward force on it, so it moves in a circle. But there is no inward force on the mud (not enough friction between the

mud and the tire!), so it moves tangential from the tire due to its inertia!

2. When on the “Swings” ride, you move away from the center of the ride as it moves around.

As the ride starts, there is an inward force on you by the rope that makes you move in a circle. BUT due to your inertia, you want to move tangent away from the circle, so your move forward as the force pulls you in, causing you to “move away” from the center.

3. Spinning pizza dough will make the pizza dough stretch out and

get bigger.The dough is being pulled in by the centripetal force, the stretchy elastic dough pulls it in. BUT the dough WANTS to move tangent, so as it spins, it tries to move straight, causes it to stretch out and become bigger.

4. You slide to the outside of the car as it turns a corner.

You are not pushed out, you do not slide! The only force is the force pulling the car inward, the centripetal force. Due to your inertia you want to keep moving straight, that is what you do, as the car slides under you.

1.Below is a diagram of a record spinning – which of the points is moving with a greater tangential speed, the inside of outside?

The outside point has a greater tangential speed.It has to cover more distance (circumference) in the same amount of time because it is farther from the center (has a greater radius).

Which picture below shows how the radius between two masses

should be measured?

Answer the following questions:1. Are astronauts weightless in outer space?

2. Is there a gravitational force between two people?

3. Is there gravity in outer space?

4. How does the gravitational force change if the mass of an object increases?

5. How does the gravitational force change if the radius of an object decreases?

No, there is gravity. It is just that since the objects are so far away, the gravitational force is very small!

Yes, there is gravity. It is just that since the objects are so small, the gravitational force is very small!

YES! There is gravity. It is just that since the objects are so far away from eachother, the gravitational force is very small!

More mass, more gravitational force! Directly Proportional

Less radius, more gravitational force!. Inversely Proportional Inverse square Law.

1) Why can’t you ‘see’ a black hole?

2) Do all stars end up becoming a black hole?

3) Will our sun someday become a black hole? What will our star become.

4) If there is a black hole at center of our galaxy how come we don’t get sucked in?

5)  If the sun were to ‘vaporize’ what did Einstein say would happen?

6) Suppose the sun did vaporize- draw Earth’s resulting motion once it no longer has the Sun’s gravitational pull on it.

7) What are two sources of evidence that black holes exist?

1)Why can’t you ‘see’ a black hole?

2)Do all stars end up becoming a black hole?

3)Will our sun someday become a black hole? What will our star become.

Because nothing can escape a black hole, not even light!!

NO!

NO!

4) If there is a black hole at center of our galaxy how come we don’t get “sucked” (pulled) in?

5) If the sun were to ‘vaporize’ what did Einstein say would happen?

6) Suppose the sun did vaporize- draw Earth’s resulting motion once it no longer has the Sun’s gravitational pull on it.

7) What are two sources of evidence that black holes exist?

because we are not within the event horizon – it’s too far away.

It would take 8 minutes for us to know, nothing, no information, can move faster than the speed of light, not even gravity!

The earth would go tangent due to its inertia.

Fast rotation of objects around the area of a black hole. Heat radiation from objects heating up as they are pulled into a black hole.

1. What is the gravitational force between two students who are standing 15m away from each other and have masses of 70.0kg and 60.0kg?

2. What is the centripetal force of a 500kg rollercoaster car being pushed around a track with a radius of 100m if its tangential speed is 25m/s?

3. What is the escape velocity on the planet Mars which as a mass of 6x1023kg and a radius of 3.6x106m?

4. A girl swings a bucket of water over her head with a 0.50m long rope. If the bucket has a centripetal acceleration of 128m/s2, how fast is the bucket moving?

5. What is the gravitational force between the Earth and the Sun? The Earth has a mass of 5.97x1024kg, the Sun has a mass of 1.99x1030kg, the distance between them is 1.50x1011m.

What is the gravitational force between two students who are standing 15m away from each other and have masses of 70.0kg and 60.0kg?

FG = G m1m2

r2

FG = (6.673x10-11Nm2/kg2) (70kg)(60kg) (15m)2

FG = (6.673x10-11Nm2/kg2) (4200kg2) (225m2)

FG = 1.25x10-9N

FG = ?r= 15mm1 = 70kgm2 = 60kg

FG = (2.80x10-7Nm2) (225m2)

What is the centripetal force of a 500kg rollercoaster car being pushed around a track with a radius of 100m if its tangential speed is 25m/s?

Fc = mVt2

rFc = (500kg)(25m/s)2

100mFc = (500kg)(625m2/s2) 100mFc = (312500kgm2/s2) 100mFc = 3125N

m = 500kg

Vt = 25m/s

Fc = ?

r = 100m

What is the escape velocity on the planet Mars which as a mass of 6x1023kg and a radius of 3.6x106m?

Vesc = 2(6.673x10-11Nm2/kg2)(6x1023kg) (3.6x106m)

Vesc = 8.01x1013m3/s2

(3.6x106m)Vesc = 2.22x107m2/s2

Vesc = 4716m/s

√

√

√

Vesc = ?M = 6x1023kgR = 3.6x106m

A girl swings a bucket of water over her head with a 0.50m long rope. If the bucket has a centripetal acceleration of 128m/s2, how fast is the bucket moving?ac =Vt =r =

128m/s2?

0.50m

ac = Vt2

r128m/s2= (Vt)2

0.50mx 0.50m

0.50m x

64m2/s2= (Vt)2

8m/s= Vt

√ √

What is the gravitational force between the Earth and the Sun? The Earth has a mass of 5.97x1024kg , the Sun has a mass of 1.99x1030kg, the distance between them is 1.50x1011m.

FG = G m1m2

r2

FG = (6.673x10-11Nm2/kg2) (5.97x1024kg)(1.99x1030kg) (1.50x1011m)2

FG = ?mE = 5.97x1024kgmS = 1.99x1030kgr= 1.50x1011m

FG = (7.93x1044Nm2) (2.25x1022m2)

FG = 3.52x1022N