Consider the picture above. The horizontal surface has friction. Suppose the blo

Question

Consider the picture above. The horizontal surface has friction. Suppose the block A is moving to the right with an acceleration of 4m/s^2 to the right. Assume the rope is massless, unstrechable, and taut and the pulley is massless and frictionless. a) Write down the equation of motion for block A (i.e the relationship between the forces acting on the block and its acceleration.) b) Write clown the equation of motion for block B (i.e the relationship between the forces acting on the block and its acceleration.) c) Compute the tension in the rope connecting the two blocks. d) Compute the coefficient of friction.

Explanation / Answer

here,

mA = 1 kg

mB = 3 kg

let the tension in the string be T and the coefficient of friction be uk

a)

for block A

T - uk * mA * g = mA * a

T - uk * 4 * 9.81 = 4 * 4 ....(1)

b)

for block B

mB * g - T = mB * a

3 * 9.81 - T = 3 * 4 ...(2)

c)

from (2)

T = 17.43 N

the tension in the string is 17.43 N

d)

from (1)

T - uk * 4 * 9.81 = 4 * 4

17.43 - uk * 4 * 9.81 = 4 * 4

uk = 0.036

the coefficint of friction is 0.036

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