a mass of 1200 kg hung by a massless cable supported by a counterweight of mass 900 kg. You may assume the gravitational acceleration to be 10 m/s2. Determine the magnitude of the acceleration (in m/s2) of the 1200 kg mass and also the magnitude of the tension (in N) in the cable. Show your workings clearly.
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Answer:
T = 10285.71 N
a = 1.4286 m/s²
Explanation:
Data:
Mass of first body = M1 = 1200 kg
Mass of first body = M1 = 900 kg
Gravitational acceleration = g = 10 m/s²
Required:
Tension in the cable = T = ?
Acceleration of body = a = ?
Calculation:
we know that
T = ( 2 × M1 × M2 × g ) / ( M1 + M2 )
Putting values we get
T= (2×1200×900×10) / (1200 + 900)
T= (21600000 / 2100 = 10285.71 N
So
T = 10285.71 N
NOW
We know that
a = ( M1 - M2 ) × (g) / ( M1 + M2 )
Putting values we get
a = (1200 - 900)(10) / (1200+900)
a = 3000 / 2100 = 1.42857
So
a = 1.4286 m/s²
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