An object with mass m_{1} = 3.70 kg, rests on a frictionless horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass m_{2} = 10.8 kg, as shown in the figure.
Two objects labeled m_{1} and m_{2} are attached together by a cable.
(a) Find the magnitude of the acceleration of each object.
a_{1}= | |
a_{2}= |
(b) Find the tension in the cable.
N
(a)
The given two masses are connected by the same cable so they
have the same acceleration:
The total mass of the system is
M = m1+m2
= 14.5 kg
The net force on the system is due to the force of gravity on the second hanging block.
Calculate the acceleration of the blocks by applying Newton' second law.
m2*g = M*a
a = 9.81*10.8/(14.5)
= 7.31 m/s2
a1=7.31 m/s2
a2=7.31 m/s2
(b)
Calculate the tension in the cable by applying Newton's second low on mass 2.
m2*g-T = m2a
T= m2*g-m2*a
= 9.81*10.8 - 10.8*7.31
= 27 N
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