What is the input force?     (b) What is the distance through which the input piston moves?

A mouse can have a mass 25 g and an elephant a mass of 7500 kg. What is the ratio D2 : D1 so that the elephant is supported by the mouse in this hydraulic system? Elephant Mouse D, D2

P

a. Compare the size of the force placed on your bicep muscle to the force of the 20 lb dumbbell lifted by your hand. Using the concept of torque, which force is greater and explain why the two forces are not identical.  b. Does the force placed on your bicep muscle change as you curl the weight closer toward your body? (In other words, is the force on your muscle different when your forearm is 90° to your upper arm than when it is 45° to your upper arm?) Explain your answer using torque.

The brake system in most cars makes use of a hydraulic system. This system consists of a fluid filled tube connected at each end to a piston. Assume that the piston attached to the brake pedal has a cross sectional area of 0.6 cm2 and the piston attached to the brake pad has a cross section area of 2.4 cm2. Determine the force at the brake pad, if you apply a force of 10 N to the piston attached to the brake pedal. Please show the formulae, the calculations, all the steps.

The maximum pressure a fluid power cylinder can sustain is 34 MPa. Compute the minimum diameter, in mm, necessary for the piston to exert a force of 50 kN.

4) This Atwood's machine includes two blocks connected by a cable, going over a pulley without slipping. Block 1 (30.0 kg) is connected to a spring (70.0 N/m), and slides on a horizontal surface with a coefficient of kinetic friction of 0.0100. Block 2 is 50.0 kg, and hangs vertically from the cable. The pulley is a disk with a radius of 0.500 m, and its moment of inertia about the center of mass is 10. 0 kg-m“. a) Draw the three free body diagrams, and write out Newton's 2nd Law for each. b) Derive the equation of motion (inhomogeneous 2nd order ODE) for this system. c) Use u-substitution to rewrite this as a homogeneous 2nd order ODE. d) Assume the position x as a function of time t is of the form x(t) = A cos (wt + p) I disk for undamped natural frequency w, phase angle P, and amplitude A. The initial conditions are: x(0) v(0) = -3. 00 m/s. Solve for the position of the mass as a function of time (you need to solve for w, 4, and A). = 2. 00 m and Mz

11. Ignoring friction, the equation E x ED = R x RD is true for all three classes of levers. Use this equation to find the effort indicated by the diagram of the Class III lever shown below.

2. For the system below: a. Give an equation of motion for h. Note that the system has two inputs, p1 and p2. b. When h= 5, give the force exerted on the bottom of the tank. (Assume that the width and height of the opening at the bottom of the tank is negligible. The area of the bottom of the tank is A). h PA PI P2 PA R

1. The piston hydraulic system can lift very heavy objects with a force significantly lower than that of direct lifting. Imagine a system in which the cross-sectional area of the piston is rectangular rather than a typical circle. The cross-sectional area of the small piston is 20 cm × 40 cm, while the cross-sectional area of the large piston is 2.5 meters × 6 meters. (a) How much force would need to be applied to the smaller piston to lift a 1300-kg car? (Ignore any height differences in the fluid) (b) Use proportional reasoning, order of magnitude, and/or related quantities sense-making techniques to determine if your answer to (a) is reasonable?