Two ob ects are connected by a light string that passes over a frictionless pull
ID: 1579838 • Letter: T
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/sExplanation / 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