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 = 38.0°. The objects are released from rest, and m2 slides 1.70 m down the slope of the incline in 4.70 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

when second mass slides down

m2 = 9.00 slides down 1.7 m in 4.6 sec

use the kinemtaic equation S = ut + 1/2 at^2

initially it was at rest so u = 0

1.7 = 0 + 1/2 * a * (4.6)2

a = 1.3 x 2 / (4.6)2 = 0.369 m/s2

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now along the incline, apply Net Downward Force = Mg

M g(sin 38) - T = ma

9*9.81 * (0.695) -T = 9*0.369

T = 58.04 N

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use the formula for friction as

m2g sin 38 - m1g - u * m2 g* cos 38 = (m1+m2) a

9 * 9.8 * sin 38 - 4*9.8 -u *9*9.81* cos 38 = (9+4)* 0.369

u = 0.148

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