Final answer:
The power output of the electric motor during the brake test is calculated using the formula for power in terms of torque and angular velocity. After computing the torque and converting the angular speed to rad/s, the power is found to be approximately 7.396 kW, which does not match any of the given options.
Step-by-step explanation:
To calculate the power output of an electric motor during a brake test, we can use the formula for power in terms of torque and angular velocity. In this scenario, two balances, S1 and S2, read 440N and 87N respectively. The effective diameter of the pulley is 500mm, and the motor operates at a speed of 800 revolutions per minute (rev/min).
The torque (τ) exerted by the motor can be calculated using the net force on the pulley and the radius (r) of the pulley:
τ = (F1 - F2) × r
where F1 is the force from S1, F2 is the force from S2, and r is the radius of the pulley:
r = diameter / 2 = 500mm / 2 = 250mm = 0.25m
τ = (440N - 87N) × 0.25m = 353N × 0.25m = 88.25 N·m
Next, we convert angular speed from rev/min to radians per second (rad/s):
ω = angular speed in rad/s = (angular speed in rev/min) × (2π rad/rev) × (1 min/60s)
ω = 800 rev/min × 2π rad/rev × 1/60 s/min = approximately 83.78 rad/s
Power (P) can now be found by multiplying the torque by the angular velocity:
P = τ × ω
P = 88.25 N·m × 83.78 rad/s = approximately 7396.10 W or 7.396 kW
Since none of the options provided in the question matches the calculated value, there may be an error in the question or in the calculation. It's important to review the steps and ensure that all units and calculations are proper.