A massless inextensible cord pulls on a 10 kg block on a rough surface. The cord

Question

A massless inextensible cord pulls on a 10 kg block on a rough surface. The cord is at an angle of 30 degrees above the horizontal. If the tension T = 40 N in the cord is the maximum tension possible before the mass will slide, then...

a) Choose an x-y coordinate system and write equations for the x and y components of the forces.

b) What condition must be imposed the accelerations to insure the block does not slide?

c) Find the normal force exerted on the block by the table. Why is the normal force not equal to the weight of the block?

Explanation / Answer

a) let the friction coefficent be

TCos(30) - N = ma

N = mg-TSin(30)

b) the force must be such that TCos(30) - N = ma =0

c)

40Cos(30) - N = 0

N = 10*9.8 - 40Sin(30) = 78 N

=> so it is less because of the component of force that is pulling is in vertical direction

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