In: Physics
A 1800kg elevator accelerates upward at 1.40m/s2 for 10.0m , starting from rest.
How much work does gravity do on the elevator?
How much work does the tension in the elevator cable do on the elevator?
Use the work-kinetic energy theorem to find the kinetic energy of the elevator as it reaches 10.0m .
What is the speed of the elevator as it reaches 10.0m ?
Here ,
work done by gravity = -mg * h
work done by gravity = -1800*9.8 * 10
work done by gravity = -176400 J
the work done by gravity is -176400 J
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tension in the cable is
T = 1800 *(9.8 + 1.40)
T = 20160 N
work done by tension = T*d
work done by tension = 20160 * 10
work done by tension = 201600 J
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Using work energy theorum
kinetic energy = 201600 - 176400
kinetic energy = 25200 J
the kinetic energy of the elevator is 25200 J
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now,
0.5 * m * V^2 = KE
0.5 * 1800 * v^2 = 25200
v =5.3 m/s
the speed of the elevator is 5.3 m/s