Objects of masses m 1 = 4.00 kg and m 2 = 9.00 kg are connected by a light strin

Question

Objects of masses m1 = 4.00 kg and m2 = 9.00 kg are connected by a light string that passes over a frictionless pulley as in the figure below. The object m1 is held at rest on the floor, and m2 rests on a fixed incline of ? = 43.0?. The objects are released from rest, and m2 slides 1.80 m down the slope of the incline in 5.00 s.

(a) Determine the acceleration of each object. (Enter the magnitude only.)
m/s2

(b) Determine the tension in the string. (Enter the magnitude only.)
N

(c) Determine the coefficient of kinetic friction between m2 and the incline.

Explanation / Answer

SFy = n - m2gcos 43° = 0 (n is the normal force) SFx = m2gsin43° - fk - T = m2a (where fk is the kinetic friction, T is tension of the string) Equation for m1: SFy = T - m1g= m1a Step 2: Combine these equations to cancel Tension: m2gsin43° - fk - T = m2a AND T - m1g= m1a And we get: m2gsin43° - fk -T + T -m1g = m2a + m1a m2gsin43° - fk -m1g = m2a + m1a m2gsin43° - µk (m2g cos 43°) -m1g = a(m2+ m1) (9kg)(9.8m/s^2)(sin43°) - µk(9kg)(9.8m/s^2)(cos43°) - (4kg)(9.8m/s^2) = 0.145 m/s^2 (9kg+4kg) 51.84N-µk71.36N - 39.2N=1.885N µk = 0.151

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