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

= 36.0°.

The objects are released from rest, and

m2

slides 1.55 m down the slope of the incline in 3.85 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

Here ,

a)

let the acceleration is a

Using second equation of motion

d = 0.5 at^2

1.55 = 0.5 * a * 3.85^2

solving for a

a = 0.209 m/s^2

the acceleration of each object is 0.209 m/s^2

b)

let the tension is T

T - m1 * g = m1 * a

T - 4 * 9.8 = 4 * 0.209

T = 40.04 N

the tension in the string is 40.04 N

c)

Now , for m2

m2*g * sin(theta) - T - u*m2*g * cos(theta) = m2 * a

9 * 9.8 * sin(36) - 40.04 - u * 9 * 9.8 * cos(36) = 9 * 0.209

solving for u

u = 0.14

the coefficient of friction between slope and mass block is 0.14

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