Two objects are connected by a light string that passes over a frictionless pull
ID: 1325077 • Letter: T
Question
Two objects are connected by a light string that passes over a frictionless pulley as shown in the figure below. Assume the incline is frictionless and take m1 = 2.00 kg,m2 = 7.10kg, and ? = 50.5.
(b) Find the magnitude of the accelerations of the objects.
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 2.25 s after being released from rest.
m/s
Explanation / Answer
T - m1 g = m1 a
m2 g * sin theta - T = m2 a
T = m1 (g + a)
m2 g sin theta - m1 (g + a) = a(m1 + m2)
a = g [(m2 sin theta - m1) / (m1 + m2)]
= 9.8 [(7.10 * sin 50.5 - 2) / (2 + 7.10)]
= 3.75 m/s2
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T = g [m1 m2 / m1 + m2] * (1 + sin theta)
= 9.8 [2 * 7.10 / 2 + 7.10] * (1 + sin 50.5)
= 27.1 N
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Because the string does not stretch, the speed of both objects are the same. Because the acceleration is constant
v = at + v0
= 3.75 * 2.25 = 8.44 m/s