Problem 1 Friday: A shopping cart, with a mass of 70 kg, is standing on a ramp that's inclined 37 degrees. The ramp is 4.2 m long. Ignore any resistance to the motion from the wheels or air.
a.) Draw the free body diagram of the cart.
b.) Find the component of gravity perpendicular to the ramp.
c.) Find the component of gravity parallel to the ramp.
d.) Find the magnitude of the normal force.
e.) What is the cart's speed at the end of the ramp?
Problem 2 Friday: Max likes to slide across the floor on her belly. Max has a mass of 15 kg. Max is a corgi. She's traveling at 5.2 m/s when she enters the kitchen and begins to slide. Friction opposes her motion, and she slides for 3 m before stopping. What is the magnitude and direction of the friction force she feels?
Problem 3 Friday: Tina the horse pulls a sled. Tina's harness is 2 m above the ground, and the rope (10 m long) is connected from the harness to the base of the sled. The sled has a mass of 300 kg. Tina can exert 700 N of force along the rope. Friction supplies 30 N of force opposing the motion.
a.) Draw the free body diagram for the sled.
b.) What is the horizontal acceleration of the sled?
c.) If the length of the rope were halved, what would the horizontal acceleration of the sled be?
Problem 4 Friday: Tim doesn't know it, but the only strap to his backpack is about to break. It is currently only able to provide 50 N of force to hold his stuff. Its contents have a mass of 5 kg. He gets in an elevator that, with a constant acceleration, goes up 3 m in 5 s. Does his strap make it? Compute the total force on the strap during the acceleration.
Problem 5 Friday: Two astronauts are facing each other on the International Space. They are initially at rest with each other and the space station. The taller one has a mass of 85 kg, and the shorter one has a mass of 75 kg. The taller astronaut pushes the shorter one, who experiences an acceleration of 4.9 m/s^2.
a.) What is the magnitude of the force on the shorter astronaut?
b.) What is the magnitude of the force on the taller astronaut?
c.) If they push on each other for 0.2 s, compute the velocity of each astronaut.