Two ob ects are connected by a light string that passes over a frictionless pull

Question

Two ob ects are connected by a light string that passes over a frictionless pulley as shown n he igure below. Assume the incli els friction ess and take ml 20 k. m2 5A0 an %, miz (a) Draw free-body diagrams of both objects. Browse.. Score: 1 out of 1 Comment: (b) Find the magnitude of the accelerations of the objects Your response differs from the correct answer by more than 10%. Double check your calculations. m/s2 (c) Find the tension in the string. Your response differs from the correct answer by more than 10%. Double check your calculations. N (d) Find the speed of each object 1.75 s after being released from rest m/s

Explanation / Answer

m1 = 2 Kg

m2 = 5.4 Kg

= 56.5 degree

(b)

From Newton's law of motion :

For mass m1,      

T - m1g = m1 a -------------(1)

For mass m2,

m2g sin - T = m2 a -------------(2)

Add (1) and (2), then we get

( T - m1g) + (m2g sin - T) = m1a + m2a

- m1g + m2 g sin = (m1 + m2)a

a = [m2 g sin - m1g ]/(m1 + m2)

a = [(5.4*9.81*sin(56.5) - (2*9.81)] / (2 + 5.4)

a = 3.311 m/s^2

(c)

Tension in the string,

T = m1(g + a)    [from eqn(1)]

T = 2(9.81 + 3.311)

T = 26.2424 N

(d)

The speed of each object 1.75 s after being released from rest = a*t

v = (3.311 m/s^2)(1.75 s)

v = 5.794 m/s

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