The front left corner of a 1500-kg vehicle strikes a rigid

Question

Question 1) A truck is stopped on a 15% grade. For some reason, the transmission is shifted into neutral with the parking brakes off so the vehicle can free roll down the constant slope. Assume the rotational intertia of the drivetrain to be negligible. Assume wind and rolling resistance to be negligible.

a) How fast will the truck be going after it travels 100 meters along the surface?

b) How fast will the truck be going after 10 seconds?

Question 2) Two rigid cylinders, #1 and #2, are rolled down a rigid slope m a distance d without slipping. They both have the same mass, but one has a radius r₁ and the other has a larger radius r₂.

a) Which one will reach the bottom first? Circle one: #1, or #2

b) Determine the symbolic ratio of speeds of the two cylinders after a specific distance is traveled. In other words, determine a simplified expression for v₁/v₂ in terms of m, d, r₁ and r₂. You are proving your answer to part a.

Question 3) An accelerometer is connected to a 20-lb frictionless linear sled and records the following accelerations.

a) What is the most likely change in velocity in miles per hour?

b) What is the change in kinetic energy of the sled?

c) How much work was done to the sled?

Question 4) A baseball bat has a "sweet spot" that corresponds to the batter feelings little as he or she strikes that ball. If the bat is 32 inches long, weight 34 ounces, has a moment of inertia I_G = 0.0413 slug-ft², the center of grip is δ = 3 inches, and l = 23.5 inches, then determine the value of d such that the reaction force at O is zero in the direction parallel to impact. Assume that bat pivots about point O.

Question 5) The front left corner of a 1500-kg vehicle strikes a rigid bridge support and moves off to the right at an angle of 30 degree from the direction of impact. It was determined that the impact velocity was 88 km/h (at 0 degrees) and the Δv in the x-direction (0 degrees from the direction of impact) was -37 km/h. Neglect any effects of rotation or friction.   

a) What is the magnitude of the Δv vector?

b) What is the direction of the Δv vector?

c) What was the post impact velocity magnitude?

d) What was the impulse magnitude acting on the vehicle?

e) Was momentum conserved in this event?

f) How much kinetic energy was lost during this crash?