A block with mass 15 kg gently placed on a ramp 20o and

Question

Q1. A block with mass 1.5 kg gently placed on a ramp (θ = 20^o) and then released. The coefficients of friction are μ_k = 0.25 and  μ_s = .85.

a) Find the magnitude of the friction force.

b) Find the acceleration of the block.

Q2. Two blocks are attached to opposite ends of a massless rope that goes over a massless, frictionless pulley. One of the blocks, witrh a mass of 8.0 kg, accelerates downwars at ¾g.

a) What is the mass of the other block?

b) What is the acceleration magnitude and direction of the other block?

c) What is the tension in the rope?

Q3. An apple crate with a weight of 12.5 N accelerates from rest along a horizontal surface as the crate is pulled with a force of 24.5 N as shown in the drawing. If μ_k = 0.20, what is the:

a) Horizontal acceleration of the crate?

b) Speed of the crate after it has moved 5 m?

Q4. A 23 kg mass is connected to a nail on a frictionless table by a massless string 1.3 m long. There is no appreciable friction between the nail and the string. If the tension in the string is 51 N while the mass moves in a uniform circle on the table.

a) List the forces that act on the mass.

b) How long does it take for the mass to make one complete revolution?

c) If the maximum tension in the string is 90 N, what is the maximum speed of the mass?

Bonus Question - A block with mass m slides down a frictionless ramp (θ = 30^o) but is slowed by the drag force from a "round" parachute with cross sectional area A . If the drag coefficient for the parachute is C and the density of air is ρ and the block's speed is v, then magnitude of the drag force D = ½ ρACv², The block starts initially at rest and the speed increases until the terminal velocity is reached.

a) Draw a free body diagram for the block.

b) During the time that the speed was increasing toward the terminal velocity: (circle choices)

i) does the acceleration: stay the same, increase, or decrease

ii) does the drag force D: stay the same, increase, or decrease

c) If D = 300 N when the block is at the terminal velocity, what is the weight of the block?