Final answer:
By calculating the power output of the motor and then using that to calculate the gravitational force on the mass, we find that the mass is rising at a speed of approximately 16.09 meters per second.
Step-by-step explanation:
The question asks us to determine the speed at which a mass is rising when lifted by an electric motor with known voltage and current, and with the diameter of the shaft specified. To solve for the speed of the rising mass, we must first find the power output of the motor, then use this to calculate the lift speed.
The electric motor's power (P) is given by the product of voltage (V) and current (I): P = V x I. Substituting the given values:
P = 86 V x 11 A = 946 W (watts).
This power is used to lift the mass against gravity. The power (P) can also be expressed as the product of the force due to gravity on the mass (F) and its velocity (v): P = F x v, where F = m x g (mass times the acceleration due to gravity).
Substituting the known values and solving for v we get:
F = 6 kg x 9.8 m/s² = 58.8 N
v = P / F = 946 W / 58.8 N = 16.09 m/s
The mass is rising at a speed of approximately 16.09 meters per second.