Two blocks, each of mass = 3.00Kg , are connected by a massless rope and start s

Question

Two blocks, each of mass = 3.00Kg , are connected by a massless rope and start sliding down a slope of incline = 40.0 at =0.000s. The slope's top portion is a rough surface whose coefficient of kinetic friction is k= 0.160. At a distance d= 1.50m 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.

Two blocks, each of mass = 3.00Kg , are connected by a massless rope and start sliding down a slope of incline theta= 40.0 at =0.000s. The slope's top portion is a rough surface whose coefficient of kinetic friction is muk= 0.160. At a distance d= 1.50m 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.

Explanation / Answer

The mass of the each block is m = 3 kg
The coefficient of friction is = 0.16
The distance of the frictional surface is d = 1.5 m
The angle of inclination is = 40 degree

The forces on the incline plane are

mgsin = 3*9.8*sin40 = 18.9 N

component of weight along the incline

mgcos = 0.16*3*9.8*cos40 = 3.6 N

The net force along the incline is

F = 18.9 - 3.6 = 15.3 N

so the acceleration is

a = F/m

a = 15.3/3

a = 5.1 m/s^2

The time to travel 1.5 m is

s = 0.5at2

t = (2*1.5/5.1)

t = 0.77 s;

v = at

v = 5.1*0.77

v = 3.927 m/s

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