Two blocks are connected by a light cord over a frictionless pulley. The 9.00 kg
ID: 1784824 • Letter: T
Question
Two blocks are connected by a light cord over a frictionless pulley. The 9.00 kg block sits on an inclined table having a smooth surface (so any friction can be ignored). The block of mass M hangs off the side of the incline as shown in the figure below. Assume the system starts at rest at t=0.00s.
a) if the acceleration of the 9kg block is 2.50 m/s^2 up the incline, determine the hanging mass M and the Tension in the cord.
b)The hanging mass is changed and now the acceleration of the 9kg block is 2.50 m/s^2 but down the incline, determine the new Mass M and the new Tension in the cord.
General Physics I Quiz 7 October 26, 2017 Name_ Two blocks are connected by a light cord over a frictionless pulley. The 9.00 kg block sits on an inclined table (see figure below for angle of the incline) having a smooth surface (so any friction can be ignored). The block of mass M hangs off the side of the incline as shown in the figure below. Assume the system starts at rest at t-0.00s. a) If the acceleration of the 9kg block is 2.50 m/s' up the incline, determine the hanging mass hangin ma ss 35° b) The hanging mass is changed and now the acceleration of the kg block is 2.50 m/s bu down the incline, determine the new Mass M and the new Tension in the cord.Explanation / Answer
Given,
m1 = 9 kg ;
a)a = 2.5 m/s^2
We need to find tension T and mass m2
for m1 and m2 we can write
T - m1g sin(theta) = m1a
m2g - T = m2 a
solving the above two eqn simultaneously for a we get,
a = (m2g - m1 g sin(theta))/(m1 + m2)
2.5 (9 + m2) = m2 x 9.8 - 9 x 9.8 x sin35 = 9.8 m2 - 50.6
22.5 + 2.5 m2 = 9.8 m2 - 50.6
m2 (9.8 - 2.5) = 22.5 + 50.6 = 73.1
m2 = 73.1/7.3 = 10.01 kg
T = m2 (g - a) = 10.01 (9.8 - 2.5) = 73.1 N
Hence, T = 73.1 N and m2 = 10.01 kg
b)a = -2.5 m/s^2
using the above derived formula
-2.5 (9 + m2) = 9.8 m2 - 50.6
-22.5 - 2.5 m2 = 9.8 m2 - 50.6
m2 (9.8 + 2.5) = 50.6 - 22.5
m2 = 2.28 kg
T = 2.28 (9.8 + 2.5) = 28.04 N
Hence, m2 = 2.28 kg ; T = 28.04 N