1. As shown in the figure below, a uniform beam is supported by a cable at one e

Question

1. As shown in the figure below, a uniform beam is supported by a cable at one end and the force of friction at the other end. The cable makes an angle of ? = 30°, the length of the beam is L = 5.00 m, the coefficient of static friction between the wall and the beam is ?s = 0.500, and the weight of the beam is represented by w. Determine the minimum distance x (in meters) from point A at which an additional weight 2w (twice the weight of the rod) can be hung without causing the rod to slip at point A.

-Calculate the linear acceleration of a car (in m/s2, the 0.300-m radius tires of which have an angular acceleration of 12.0 rad/s2. Assume no slippage.

-For the car in the previous problem, how many revolutions do the tires make in 2.50 s if they start from rest?

- What is their final angular velocity of the tires in the previous question? (in rad/s)

-What is the final velocity of the car in the previous question? (in m/s)

Explanation / Answer

)

Horizontally, for tension T and normal force on beam Fn, we've got

Fn = Tcos30º = 0.866T

We know that at the threshold, Ff = u*Fn = 0.500 * 0.866T = 0.433T

where Ff is the friction force at the beam

Vertically, we've got Ff + Tsin30º = 0.433T + 0.5T = 0.933T = w + 2w = 3w

so T = 3.215w

Finally, consider the moment about the left end of the beam.

It must be zero, or the beam would rotate.

Summation of M = 0 = Tsin30º * L - w*L/2 - 2w*x = 3.215w * 0.5 * L - w*L/2 - 2w*x

w cancels from all terms:

1.1077L = 2x

x = 0.554L

Since L = 5 m,

x = 2.77 m

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