Two blocks are positioned on surfaces, each inclined at the same angle theta 67.

Question

Two blocks are positioned on surfaces, each inclined at the same angle theta 67.6 degrees with respect to the horizontal. The blocks are connected by a rope which rests on a frictionless pulley at the top of the inclines as shown, so the blocks can slide together. The mass of the black block is 1.4 kg, and the coefficient of friction for both blocks and inclines is 1.52. Assume gravity is g=9.8 m/s2.

A) What must be the mass of the white block if both blocks are to slide to the left at an acceleration of 1.5 m/s2?

B) Now re-do part (A) above, but now assuming no friction at all on either incline. So in the absence of friction, what must be the mass of the white block such that both blocks slide to the left at an acceleration of 1.5m/s2?

Explanation / Answer

here,

theta = 67.6 degree

mass of black box , m1 = 1.4 kg

u = 1.52

a)

for the block to move left at a = 1.5 m/s^2

(m2 - m1 ) * g * sin(theta) - u * g * ( m1 + m2) * cos(theta) = (m1 + m2) * a

( m2 - 1.4) * 9.81 * sin(67.6) - 1.52 * 9.81 *( 1.4 + m2) * cos(67.6) = (1.4 + m2) * 1.5

m2 = 12.1 kg

the mass of the white block is 12.1 kg

b)

when there is no frictional force

for the block to move left at a = 1.5 m/s^2

(m2 - m1 ) * g * sin(theta) = (m1 + m2) * a

( m2 - 1.4) * 9.81 * sin(67.6) = (1.4 + m2) * 1.5

m2 = 1.95 kg

the mass of the white block is 1.95 kg

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