Unit 3: Circular Motion & Gravitation
What is Newton's law of gravitation?
F=Gm₁m₂/r²
An artificial satellite orbits Earth at a speed of 7800m/s and a height of 200km above Earth's surface. What is the acceleration of the satellite due to gravity?
Less than g but greater than 0
A moon of mass 1×10²⁰ kg is in a circular orbit around a planet. The planet exerts a gravitational force of 2×10²¹ N on the moon. What is the centripetal acceleration of the moon?
20m/s²
An astronaut with mass m is within a satellite that orbits Earth at a height H above its surface. Earth has a mass M and radius R. What is the correct expression for the gravitational force exerted on the astronaut by Earth?
(GMm)/(R+H)²
An object is placed on a rotating disk 0.10m from the center and moves with a constant tangential velocity of 0.60m/s, the force of gravity exerted on the block is 2N. What is the force of friction on the object? (Hint:v=√μgr)
0.734N
A 100kg cart goes around the inside of a vertical loop of a roller coaster. The radius of the loop is 3m and the cart moves at a speed of 6m/s at the top. What is the force exerted by the track on the cart at the top of the loop?
220N
Planet X has twice Earth's mass and three times Earth's radius. What is the magnitude of the gravitational field near Planet X's surface?
2.17N/kg
A 2kg object is a distance of 10,000,000 m away from the center of Earth, which has a mass of nearly 6x10²⁴kg. what's the approximate gravitational field strength of Earth's gravitational field at the location of the 2kg object?
4N/kg
A student conducts an experiment in which a 0.5kg ball is spun in a vertical circle from a string of length 1m. The student uses the equation Fₜ=mv²/r to predict the force of tension exerted on the ball when it reaches the bottom of the circular path at a different tangential speed for multiple trials. When the experiment is conducted, the student uses a force probe to measure the actual force of tension exerted on the ball. A) Why is the predicted force of tension different than the actual force of tension? B) What would be the proper equation to use?
A) The student did not account for the downward force due to gravity at the ball's lowest point along its circular path B) Fₜ=(mv²/r)+(mg)
What is the equation for centrifugal force?
Centrifugal force does not exist
Which law has the same equation as Newton's law of gravitation with different variables?
Coulomb's law for electrostatic forces: F=kq₁q₂/r²
What is the formula for centripetal force?
F = ma = mv²/r
What is the force of gravity between two roughly spherical objects of masses m₁ and m₂?
G(m₁m₂)/r² when r is the distance between the centers of the two objects.
A satellite of mass m and speed v moves in a stable, circular orbit around a planet of mass M. What is the radius of the satellite's orbit?
GM/v²
A small block slides without friction along a track toward a circular loop. The block has more than enough speed to remain firmly in contact with the track as it goes around the loop. What is the magnitude of the block's acceleration at the top of the loop?
Greater than g
A planet of mass m orbits a star of mass M, where m<<M. The orbit is circular, its radius is r, and its period is T. Which of the following statements are true? (Pick all that apply) I. The orbital speed equals 2πr / T II. The gravitational force equals GMm/r² III. If the orbital radius r were greater, T would also be greater.
I, II, and III
What happens to the gravitational pull of an object as it gets farther away from Earth?
It changes by a factor of the inverse square distance of the radius (distance from the centers of both objects)
A toy car enters a vertical circular loop with an initial velocity and moves completely around the loops without friction. If the car has no means of self propulsion, describe the car's acceleration when it's at the leftmost point of the circle.
It has components both downward and toward the center of the circle
What is uniform circular motion?
Motion in a circular path at a constant speed
If 1 kg of steel and 3 kgs of copper are dropped from the same height, which hits the ground first?
Neither, they hit at the same time
What direction is the linear velocity of an object moving with uniform circular motion?
Tangential to the point it's at in the circle
A ball of mass M swings in a horizontal circle at the end of a string of radius R at a constant tangential speed. A student gradually pulls the string inward such that the radius of the circle decreases while keeping the tangential speed of the ball constant. Describe the acceleration of the ball
The acceleration starts increasing slowly then starts increasing faster
A planet has two moons, Moon A and Moon B, that orbit at different distances from the planet's center, as shown. Astronomers collect data regarding the planet, the two moons, and their obits. The astronomers are able to estimate the planet's radius and mass. The masses of the two moons are determines to be 2M for Moon A and M for Moon B, It is observed that the distance between Moon B and the planet is two times that of the distance between Moon A and the planet. How does the force exerted from the planet on Moon A compare to the force exerted from the planet on Moon B.
The gravitational force exerted from the planet on Moon A is eight times larger than the gravitational force exerted from the planet on Moon B
What is centripetal acceleration?
The net acceleration of an object moving in a circle, it is NOT an acceleration itself
What is centripetal force?
The net force acting upon an object as it travels in uniform circular motion
A cart of mass m rolls past the circular bottom of a hill. Describe the normal force of the cart at the bottom of the hill.
The normal force is greater than mg because the cart is experiencing an upward acceleration
An object of unknown mass is swung in a vertical circle at the end of a light string. A measurement is made of the object's tangential speed at the bottom of the circular path. A student must determine the tension in the string at the bottom of the circular path. What measurements, in conjunction with the object's tangential speed, are required to determine the tension in the string?
The objects mass and the diameter of the circular path
Where does the centripetal acceleration always point?
Toward the center of the circular path
An object has a weight W when it is on the surface of a planet of radius R. What will be the gravitational force on the object after it has been moved to a distance of 4R from the center of the planet?
W/16
What is a Newton?
kg*m/s²
What is N/kg equal to?
m/s²
A ball of mass m is attached to a vertical rod by two massless strings. The rod is rotated about its axis so that both strings are taut, with tensions T₁ and T₂ respectively. The ball rotates in a horizontal circle of radius r with speed v. What is the magnitude of the net force on the ball?
mv²/r
Two massive, positively charged particles are initially held a fixed distance apart. When they are moved farther apart, the magnitude of their mutual gravitational force changes by a factor of n. What is the factor by which the magnitude of their mutual electrostatic force changes?
n
What's the equation for centripetal acceleration?
v²/r
Two satellites are in circular orbits around Earth. Satellite 1 has speed v₁ . Satellite 2 has an orbital radius nine times that of satellite 1. What is the speed of satellite 2?
v₁/3