Problem 1 The crate has a weight of 100 lb and is initially at rest. The force P is sufficient for the crate to move down the incline at a velocity of 5t. The coefficient of kinetic friction μk = 0.25. a) Draw a complete Free Body Diagram. b) Write the equations of motion for your selected coordinates. The only variables should be unknowns. c) Solve for the required force P. d) What is the velocity when the crate has traveled one foot. 30° P

Q1(A) At a carnival, a daredevil rides a motorcycle around and around the "wall of death," a wooden cylinder with vertical walls. The radius of the cylinder is R = 5.0m, and the coefficient of static friction between the motorcycle's tires and the walls is us = 0.90. a) Draw a force diagram for the motorcycle. b) What is the minimum speed at which the motorcycle can ride in a horizontal circle without sliding down to the bottom? Q1(B) An elevator and its load have a combined mass of 1100kg, and is suspended from a strong metal cable. The elevator is initially moving upward at 7.00m/s; it slows to a stop with a constant acceleration in a distance of 20.0m. What is the tension T in the elevator cable during this process?

The rotation axis of the uniform cylinder is constrained by a frictionless slot. The cylinder is at rest when it is lowered onto the conveyor belt, which has a constant translational velocity of 20.0 ft/s. The coefficient of friction between the belt and the cylinder is 0.400.a) Calculate the maximum angular velocity of the cylinder.b) The distance traveled by the belt during the time the cylinder is accelerating to its maximum angular velocity

A particle P of mass m = 1 kg arrives at point with a horizontal velocity vo and starts rolling down a circle with radius R = 1 m. The particle is attached to the point O by means of a linear spring of stiffness k = 50 N/m that is unstretched when the particle is at O. Assume that during the motion of P along the circle, the spring follows the circle. Let N = {ĥ, ny} be a fixed reference frame as shown in the figure and let B = {b, by} be a reference frame attached to P so that b is tangent to the circular path and by is perpendicular to the circular path. For convenience, take g = 10 m/s² in this question. ny 1/ nx IP

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The vehicle shown starts from rest at the bottom of the hill and accelerates up the hill due to the force FR from the road. Note that this is a static friction force and is not dissipative. Vrop = 9.7 m/s m = 1600 kg h = 50 m FR = 7300 N 0 = 25° A) If the vehicle reaches the top of the hill with the speed shown, how much thermal energy is dissipated in the process? B) Assuming that air drag, Fang , is the only dissipative force during this process, try to estimate the cross-sectional area of the vehicle "seen" by the air. In the formula for air drag, regard the car's speed as being a constant v = 5.0 m/s (this speed is roughly half of the starting and ending speeds). Use C = 0.5 for the drag coefficient and p = 1.25 kg/m³ for air density.

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4. For this series of 4 questions, two blocks, A and B, are connected using the cable and pulley system as shown. (The cable and pulley system is friction-less and weight- less.) The coefficient of kinetic friction between block A and the inclined plane is μk = 0. 2. Initially the blocks are moving but eventually come to stop. You will be asked to solve for different things. Please pay attention: the numbers may change from problem to problem since they are randomized. 3) If the blocks and the cable-pulley system are considered as one system, during this process from the blocks moving to them coming to stop, which forces are doing work to this system? A B C D Weight of block B. Weight of block A. Friction between block A and the incline plane. Tension force in the cable connecting to block B. Tension force in the cable connecting to block A.

Dynamics 1-There is a spring with the initial length of 0.4 m and its constant is 200 N/m. The slider attached to this spring which is at position A. The mass of the slider is 3 kg and it is released from the rest at A. If the system is on the vertical plane and there is no friction: A) Find the reaction force from the rod on the slider at position C B) What is tangential acceleration of the slider at position C? C) Determine the velocity of the slider at position B. 40° 0.8 m B. 0.6 m www

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