Question

Two blocks, each of mass m = 6.00 kg , are connected by a massless rope and start sliding down a slope of incline θ = 36.0 ∘ at t=0.000 s. The slope's top portion is a rough surface whose coefficient of kinetic friction is μk = 0.300. At a distance d = 1.90 m from block A's initial position the slope becomes frictionless. What is the velocity of the blocks when block A reaches this frictional transition point? Assume that the blocks' width is negligible.

Answer 1

Solution,

Given,

Mass, m = 6 kg

Distance, d = 1.9 m

Angle, theta = 36 degree

Forces,

mgsin(thet) = 6 x 9.8 x sin36 = 34.56 N

component of weight along the incline

u mg cos(theta) = 0.3 x 6 x 9.8 x cos36 = 14.27 N

Net force along the incline,

F = 34.56 - 14.27 = 20.29 N

Acceleration, a = F/m = 20.29/6 = 3.38 m/s^2

Using kinematic equation,

s = 0.5 at2

Time, t = sqrt(2 x 1.9/3.38) = 1.06 sec

Again using kinematic equation,

v = u + at

Velocity, v = 0 + 3.38 x 1.06 = 3.58 m/s

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