An 60 kg plank, 15 m long, has supports at locations X1=4 m and X2=12 m...

An 60 kg plank, 15 m long, has supports at locations X1=4 m and X2=12 m along the plank. Two additional forces F3=20 N and F4=25 N act at the points X3=2 m and X4=10 m along the plank, making angles of 30 degrees and 60 degrees with respect to the vertical.

a) from x-equilibrium, determine the value of F4,

b) from rotational equilibrium, determine the support forces N1 and N2 acting at the location of the two supports, taking into account the mass of the plank itself,

c) show that your answers are correct by demonstrating that they satisfy equilibrium in y-.(i.e., that the sum of the forces in the y-direction are zero, since the plank is stationary).

Expert Solution

genius_generous answered 1 year ago

Consider a long (length = 15 m) uniform wooden beam (mass = 60 kg) attached horizontally...

Consider a long (length = 15 m) uniform wooden beam (mass = 60 kg) attached horizontally to a wall that can only support a vertical load ( The horizontal component of the force of the wall on the beam is identically zero). There is a chandelier (mass = 40 kg) hanging at a distance = 4.21 meter from the end of the beam that is attached to the wall. There is a vertical cable hanging down from the ceiling that...

Let the utility function be given by u(x1, x2) = √x1 + x2. Let m be...

Let the utility function be given by u(x1, x2) = √x1 + x2. Let m be the income of the consumer, P1 and P2 the prices of good 1 and good 2, respectively. To simplify, normalize the price of good 1, that is P1 = £1. (a) Write down the budget constraint and illustrate the set of feasible bundles using a figure. (b) Suppose that m = £100 and that P2 = £10. Find the optimal bundle for the consumer....

4.Maximize: Z = 2X1+ X2-3X3 Subject to: 2X1+ X2= 14 X1+ X2+ X3≥6 X1, X2, X3≥0...

4.Maximize: Z = 2X1+ X2-3X3 Subject to: 2X1+ X2= 14 X1+ X2+ X3≥6 X1, X2, X3≥0 Solve the problem by using the M-technique.

A high-speed lifting mechanism supports a 710 kg object with a steel cable 20.0 m long...

A high-speed lifting mechanism supports a 710 kg object with a steel cable 20.0 m long and 4.00 cm2 in cross-sectional area. (a) Determine the elongation of the cable. _____ mm (b) By what additional amount does the cable increase in length if the object is accelerated upward at a rate of 2.6 m/s2? _____ mm (c) What is the greatest mass that can be accelerated upward at 2.6 m/s2 if the stress in the cable is not to exceed...

Amy has utility function u (x1, x2) = min { 2(x1)^2x2, x1*(x2)^2 }. Derive Amy's demand...

Amy has utility function u (x1, x2) = min { 2*(x1)^2*x2, x1*(x2)^2 }. Derive Amy's demand function for x1 and x2. For what values (if any) of m, p1, and p2 are the goods gross complements or gross substitutes of each other?

Suppose that a firm has the p production function f(x1; x2) = sqrt(x1) + x2^2. (a)...

Suppose that a firm has the p production function f(x1; x2) = sqrt(x1) + x2^2. (a) The marginal product of factor 1 (increases, decreases, stays constant) ------------ as the amount of factor 1 increases. The marginal product of factor 2 (increases, decreases, stays constant) ----------- as the amount of factor 2 increases. (b) This production function does not satisfy the definition of increasing returns to scale, constant returns to scale, or decreasing returns to scale. How can this be? (c)Find...

Suppose an agent has preferences represented by the following utility function: u(x1, x2) = 1/4 ln(x1)...

Suppose an agent has preferences represented by the following utility function: u(x1, x2) = 1/4 ln(x1) + 3/4 ln(x2) The price of good x1 is 2, the price of good x2 is 6, and income is 40. a) What is the consumers best feasible bundle (ie, his optimal consumption bundle)? b) Interpret the consumer’s marginal rate of substitution at the best feasible bundle found in part a).

Suppose that a consumer has a utility function U(x1,x2) = x1 ^0.5 x2^0.5 . Initial prices...

Suppose that a consumer has a utility function U(x1,x2) = x1 ^0.5 x2^0.5 . Initial prices are p1 =1and p2 =1,andincomeism=100. Now, the price of good1 increases to 2. (a) On the graph, please show initial choice (in black), new choice (in blue), compensating variation (in green) and equivalent variation (in red). (b) What is amount of the compensating variation? How to interpret it? (c) What is amount of the equivalent variation? How to interpret it?

Assume a consumer has the utility function U (x1 , x2 ) = ln x1 +...

Assume a consumer has the utility function U (x1 , x2 ) = ln x1 + ln x2 and faces prices p1 = 1 and p2 = 3 . [He,She] has income m = 200 and [his,her] spending on the two goods cannot exceed her income. Write down the non-linear programming problem. Use the Lagrange method to solve for the utility maximizing choices of x1 , x2 , and the marginal utility of income λ at the optimum.

. Consider a firm that has a production function y = f(x1, x2) = 2x 1/4...

. Consider a firm that has a production function y = f(x1, x2) = 2x 1/4 1 x 1/4 2 facing input prices w1 = 2 and w2 = 4. Assume that the output price p = 8. • What will be the profit maximizing output level? -What will be the profit? • -If this firm is divided up into two equal-size smaller firms, what would happen to its overall profits? Why

Question