solve for question 2 and this is the link for the image http://postimg.org/image

Question

solve for question 2 and this is the link for the image http://postimg.org/image/x8yckk9l9/

A 5 kg ball is released as shown. 6 sec later it hits the rough surface (e = .75) whenever it bounces, Would it clear the wall ? The 199th beam of radius of 8th is supported by the edge of the table and a spring that was stretched 0.75" Before being attached at B. Determine the reactions Ax and Ay immediately upon the removal of the table. What will be the omega of the beam when it attains the horizontal configuration? Knowing that the velocity of collar D is 20 1 / sec, determine omega AD omega EB VA Remember! Velocity has to have direction. How far away from the red light should the driver going at 90 mph apply his brakes so as not to ensue any instabilities to the unsecured load he is transporting?

Explanation / Answer

Ax = horizontal raction

Ay = vertical raeaction

forces in the vertical direction

kx = spring force = 120 x 0.0625 = 7.5 lbf = 240 lb ft/s^2

x = .75 in = 0.0625 ft

as the pic was not clear i assume the mass = 19 lb

weight = mg = 19 x 32 = 608 lb ft/s^2

now

there are no horizontal forces on the bar

thus Ax = 0

Ay = kx + mg

Ay = 608 + 240

Ay = 848 lbft/s^2

now

we consider the torque produced by the forces

T= torque = I x alpha

I = moment of inertia

alpha = angular acceleration

torque due to spring force = 240 x .75 = 180

due to weight = 608 x .92 = 559.36

total torque = 180+559.36 = 739.36 lbft^2/s^2

I = mk^2

k = radius of gyration = .67 ft

I = 19 x .67^2 = 8.53 lb ft^2

T = I x alpha

alpha = T/I = 739.36 / 8.53

alpha = 86.68 rad/s^2

w = angular velocity

w^2 = 2 x alpha x theta

theta = angular displacement = 27 degrees = 0.4712 rad

w^2 = 2 x 86.68 x .4712

w = 9 rad/s

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