Gravitational Force
Two masses have a gravitational force F between them. If the mass of each is quadrupled and their separation remains the same, how much larger is the force between them?
16F
(16 times larger)
You are riding a bicycle and toss a ball straight up. Does it fall behind you, ahead of you, or back into your waiting hand?
The ball falls back into your waiting hand.
True or False (if false, correct the statement):
A ball in free fall is in dynamic equilibrium.
False.
A ball in free fall is, by definition, accelerating. Therefore, it is in non-equilibrium.
True or False (if false, correct the statement):
If a box is on an incline, you use sine of the angle of the incline to calculate the x component of gravity.
True, because the angle of the incline is the same as the angle between Fg and Fgy (so the angle is measured with respect to the vertical)
A 5kg block is sitting on a frictionless table, connected (over a pulley) to a hanging 7kg mass. When the system is released, which way will the block on the table move?
Toward the pulley / hanging mass / edge of the table
Two masses have a gravitational force F between them. If the mass of each remains the same and their separation becomes 7 times larger, what is the change in the force between them?
1/49 F
(F becomes 1/49 what is was before)
You are riding in a car and the driver slams on his brakes. Are you thrown forward, pressed back into your seat, or unaffected?
You are thrown forward. I hope you're wearing a seat belt.
True or False (if false, correct the statement):
If the sum of forces in the x direction = ma, then the sum of forces in the y direction must also = ma
False! An object can be accelerating in the x direction, but in static equilibrium in the y direction.
True or False (if false, correct the statement):
Acceleration occurs when you push on an object with more force than it applies to you.
False! The object will push back with equal force. Acceleration will occur when the sum of forces on the object does not equal zero.
If a 2 kg mass is hanging from a pulley, and another 2 kg mass is on a 45 degree frictionless ramp attached to the other end of the string, which way does the system move?
The hanging mass moves down and the mass on the ramp slides up.
What is the gravitational attraction between the Earth and our moon?
1.986 x 10^20 N
You are riding in an airplane. Suddenly, your bag of pretzels floats up to the ceiling of the aircraft, along with the belongings of several other people. What has happened?
The airplane experienced a sudden loss of altitude (it dropped abruptly).
Mr. Swart can pull a tablecloth out from under a place setting without breaking the dishes. How is this possible?
Inertia. And magic.
True or False (if false, correct the statement):
When calculating gravitational force, the radius between masses is measured from the edge of one mass to the edge of the other.
False.
Radius is measured from the center of one mass to the center of the other.
A 33 kg mass is sitting on a table. It is attached to a string that goes over a pulley and connects to a hanging mass weighing 7 kg. The table has a coefficient of friction of 0.19. Is this system in static equilibrium or non-equilibrium? If non-equilibrium, which way is it moving?
Non-equilibrium. The hanging mass is dragging the table mass across the surface of the table as the hanging mass goes down.
Three masses are in a row. The middle mass is 150 m away from each end mass. If the left mass is 10,000 kg, the middle mass is 5,000 kg, and the right mass is 15,000 kg, what is the net force on the middle mass?
7.4113 x 10^-8 N to the right.
You set a pair of sunglasses on the dash of your car. As you drive, you take a sharp left turn. The sunglasses slide across the dash to the right side of the car. What force causes the sunglasses to slide?
No force! This is an illustration of Newton's First Law. The sunglasses were in the car, speeding along with it. The car turned, and the sunglasses didn't want to change direction.
A baseball flies into a car's windshield. Which experiences greater force?
They experience the same force. But the owner of the car experiences a greater pull on their bank account.
How will your mass change if you travel to Pluto?
Mass does not change. Weight is determined by gravity.
A 27 kg mass sits on a frictionless 27 degree incline. It is attached to a string and pulley, and on the other end of the string is a hanging 13 kg mass. Which way does the system move?
The hanging mass is moving down, pulling the 27 kg mass up the ramp.
Assuming they are all in a row, the Sears Tower (not calling it by that other name) is the farthest west and weighs 199,580,643 kg. It is 1,274,760 m from the Empire State Building, which weighs 331,122,430 kg. Pretending that the Statue of Liberty is due east from the Empire State Building, it weighs 204,117 kg and is 9656 m away. What is the net force on the Empire State Building?
4.564 x 10^-5 N towards the Statue of Liberty
I am driving down the highway at 70 mph with a kleenex box, a tire iron, and my backpack in the back seat of my car. My car comes to a sudden stop. Why should I be worried?
All of the items in my back seat were traveling at 70 mph with the rest of the car. If they are not secured, they will not stop when the car does.
Nothing makes a bad day worse like a tire iron to the head.
True or False (if false, correct the statement):
An old Buick crawling along at 25 mph has less inertia than a Vespa cruising past at 45 mph.
False. Mass matters! The Buick has much greater mass, so it has greater inertia.
If a box is being pushed at a downward angle across a flat surface that does have friction, and the box is accelerating, what are the force summations in the x and y directions?
Sum Fx: FAx - Ff = ma
Sum Fy: FN - Fg - FAy = 0
A 27 kg mass sits on a 65 degree incline, which has a coefficient of friction of .41. The mass is connected by a string and a pulley to a 13 kg hanging mass. Which way does the system move when released?
The 27 kg mass slides down the ramp, pulling the hanging mass upward.