Coinsider the scenario shown in the diagram below. A box (mass m_1) is on a slop

Question

Coinsider the scenario shown in the diagram below. A box (mass m_1) is on a slope, which is inclined at an angle theta with respect to the horizontal. The box is connected via a string and pulley to a hanging weight (mass m_2). The string and the pulley are assumed to be massless and frictionless, but there is friction between the box and the incline (with coefficient of kinetic friction mu k).Find an expression for the tension T in the string as the box slides down the incline. You answer should be written in terms of m_1, m_2, theta, mu _k, and g.

Explanation / Answer

here,

frictional froce , ff = uk * N

ff = uk * m * g * cos(theta)

accelration of the blocks , a = net force /(effective mass)

a = ( m2g + m1*g*sin(theta) - uk*m*g*cos(theta) ) /( m1 + m2)

for block m2

m2*g - t = m2*a

t = m2 * ( g + a)

t = m2 * (g + ( m2g + m1*g*sin(theta) - uk*m*g*cos(theta) ) /( m1 + m2) )

t = m2 *g* (1 + ( m2 + m1*sin(theta) - uk*m1*cos(theta) ) /( m1 + m2) )

the tension in the string is t = m2 *g* (1 + ( m2 + m1*sin(theta) - uk*m1*cos(theta) ) /( m1 + m2) )

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