Chapter 5, Problem 5.46CU

1. Create a table comparing five different analogous variables for translational, rotational, electrical and fluid systems. Include the standard symbols for each variable in their respective systems.

2) Suppose that two unequal masses m₁ and m₂ are moving with initial velocities v₁ and v₂, respectively. The masses hit each other and have a coefficient of restitution e. After the impact, mass 1 and 2 head to their respective gaps at angles a and ẞ, respectively. Derive expressions for each of the angles in terms of the initial velocities and the coefficient of restitution. m1 m2 8 m1 m2 β

4. Find the equivalent spring constant and equivalent viscous-friction coefficient for the systems shown below. @ B₁ B₂ H B3 (b)

5. The cart shown below is inclined 30 degrees with respect to the horizontal. At t=0s, the cart is released from rest (i.e. with no initial velocity). If the air resistance is proportional to the velocity squared. Analytically determine the initial acceleration and final or steady-state velocity of the cart. Take M= 900 kg and b 44.145 Ns²/m². Mg -bx 2 от

9₁ A Insulated boundary Insulated boundary dx Let's begin with the strong form for a steady-state one-dimensional heat conduction problem, without convection. d dT + Q = dx dx According to Fourier's law of heat conduction, the heat flux q(x), is dT q(x)=-k dx. x Q is the internal heat source, which heat is generated per unit time per unit volume. q(x) and q(x + dx) are the heat flux conducted into the control volume at x and x + dx, respectively. k is thermal conductivity along the x direction, A is the cross-section area perpendicular to heat flux q(x). T is the temperature, and is the temperature gradient. dT dx 1. Derive the weak form using w(x) as the weight function. 2. Consider the following scenario: a 1D block is 3 m long (L = 3 m), with constant cross-section area A = 1 m². The left free surface of the block (x = 0) is maintained at a constant temperature of 200 °C, and the right surface (x = L = 3m) is insulated. Recall that Neumann boundary conditions are naturally satisfied…

1 - Clearly identify the system and its mass and energy exchanges between each system and its surroundings by drawing a box to represent the system boundary, and showing the exchanges by input and output arrows. You may want to search and check the systems on the Internet in case you are not familiar with their operations. A pot with boiling water on a gas stove A domestic electric water heater A motor cycle driven on the roadfrom thermodynamics  You just need to draw and put arrows on the first part a b and c

7. A distributed load w(x) = 4x1/3 acts on the beam AB shown in Figure 7, where x is measured in meters and w is in kN/m. The length of the beam is L = 4 m. Find the moment of the resultant force about the point B. w(x) per unit length L Figure 7 B

4. The press in Figure 4 is used to crush a small rock at E. The press comprises three links ABC, CDE and BG, pinned to each other at B and C, and to the ground at D and G. Sketch free-body diagrams of each component and hence determine the force exerted on the rock when a vertical force F = 400 N is applied at A. 210 80 80 C F 200 B 80 E 60% -O-D G All dimensions in mm. Figure 4

2. Figure 2 shows a device for lifting bricks and concrete blocks. It comprises two compo- nents ABC and BD, with a frictionless pin at B. Determine the minimum coefficient of friction required at A and D if the device is to work satisfactorily. W all dimensions in inches Figure 2 D