Center of Mass/Newton's 1st and 3rd Laws
When a rocket-propelled ship launches from the ground, it expels exhaust gas from the bottom of the ship, as shown above. Which of the following explains why the ship is able to leave the ground?
The ship exerts a downward force on the gas, and the gas exerts an upward force on the ship.
In words, describe the relationship between acceleration, mass, and force
As mass increases, the acceleration will decrease and as the force increases, the acceleration will increase
What is Newton's Universal Law of Gravitation? How can this law be used to determine the free fall acceleration due to gravity on any celestial object?
FG = (Gm1m2)/(r122)
g = (Gmobject)/(robject2)
What direction must the net force and acceleration point in order for circular motion to be maintained?
Towards the center of the circle of motion; or the centripetal direction
What direction do the new x and y axes point on an inclined plane?
The new x axis point along the incline and the new y axis point perpendicular to the incline
2 hot air balloons fly at different heights above the ground. One of mass of 750 kg is at a height of 550 meters, while the other; mass of 500 kg is directly below it at a height of 250 meters. How far above the ground is the center of mass between the balloons?
430 meters
Spiderman shoots his web at the green goblin, mass of 60 kg, and pulls him towards him at a constant speed. If Spiderman’s webs exert a force of 90 Newtons at an angle of 35 degrees, what force must the ground exert upward on the green goblin? (Assume the green goblin is dragged on the ground and doesn’t move vertically)
536.4 Newtons
The Rizzler, mass of 75 kg, and Big Justice, mass of 55 kg, stand a distance of 1.2 km apart. What is the force of gravity between the two?
1.9 x 10-13 Newtons
Hamza drives a Ferrari with a mass of m=1200 kg and is traveling around a circular track with a radius of r=50 m. The coefficient of static friction between the car's tires and the road is μs=0.4. What is the maximum speed the car can travel at without slipping?
14 m/s
A toy car starts from rest at the top of a 35 degree frictionless incline. If the incline is 2 meters long, what is the car’s velocity at the bottom of the incline?
4.74 m/s
A 40 g block and a 10 g block are placed along a track, as shown. The 40 g block is on 0 cm the mark at the left end of the track. The 10 g block is located at 50cm. At what position on the track is the center of mass of the two block system?
10 cm
Mr Composto’s 1500 kg Lamborghini is traveling at a velocity of 45 m/s. He sees a red light and he skids to a stop in 10 seconds. What is the coefficient of kinetic friction between his tires and the road?
.459
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
Sonic the Hedgehog, mass of 35 kg, travels around a vertical circular loop hill with a radius of 15 meters. At the top of the hill, Sonic feels half as heavy. What speed must Sonic have traveled at to complete this loop?
14.85 m/s
A skier starts from rest and descends down a 100m long mountain with a coefficient of kinetic friction of .2, inclined at 20 degrees. How long will it take to ski down the hill?
11.5 seconds
Ian punches Mr Composto in the face, such that his cheek (mass of .25 kg) crumples a distance of 3 cm, reaching a speed of 1.2 m/s by the end. What magntitude of force will Mr Composto's face exert on Ian's fist?
6 Newtons
In order to travel from Barbie Land into the real world, Ken, with a mass of 50 kg, must accelerate from rest to a speed of 25 m/s in 50m. What force do his roller blades need to exert on Ken in order to reach the real world?
312.5 Newtons
An astronaut of mass 80 kg is on Earth. What would be the astronaut's weight (force of gravity) at an altitude of 1000 km above Earth's surface? (Earth has a radius of 6.38 x 106)
584.4 Newtons
A penny is placed 12.0cm from the axis of a rotating record of variable speed. When the speed of the record is slowly increased, the penny remains fixed on the turntab until a rate of 40 revolutions per minute is reached, at which point the penny slides off. Calculate the coefficient of static friction between the penny and the record.
.214
A string passing over a frictionless pulley has a mass of 6 kg attached to one of its ends. To the other end a mass of 10 kg is attached. What is the acceleration of the 2 masses?
2.45 m/s2
A soccer ball of mass m1 is located at position x = 0 while a medicine ball of mass m2 = 2m1 is located at x = x0. Find the position of the center of mass of the system
2x0/3
A bag of candy, mass of 2.5 kg, is on a front porch attached to two horizontal springs (k1 = 50 N/m, k2= 60 N/m). Both springs are compressed a distance of .5 meters from their unstretched length and the bag of candy remains at rest due to static friction between the block and the surface. Determine the coefficient of static friction between the porch and the bag of candy.
2.24
Determine the free fall acceleration due to gravity on Mars. Mars has a mass of 6.42 x 1023 and a radius of a radius of 3.4 x 106 (G = 6.67 x 10-11)
3.69 m/s2
Spider-Man is swinging a metal trash can in a horizontal circle at the end of a web of length L=1.5 m. The web makes an angle of 40∘ with the vertical. The tension in the web is T=110 N, and the object is moving at a constant speed of v= 1.5 m/s. What is the mass of the trash can?
8.6 kg
The Batmobile, mass 1500 kg, sits atop a 25 meter high flat roof. The roof has a coefficient of friction of .035. Harley Quinn, mass of 120 kg, who is attached to the front via a string, jumps off the roof in an attempt to escape. What will Harley Quinn and the batmobile's acceleration be?
.408 m/s2