Final answer:
To calculate the power output required for the mechanical arm, we multiply the force (964 Newtons) by the distance (9.8 meters) to find the work done, then divide by the time (23 seconds) to find the power. The required power output for the motor is 410.75 Watts.
Step-by-step explanation:
To determine the power output required of a motor that uses a mechanical arm to push crates, we can use the formula for power, which is the work done over time. The work done by the arm in pushing the crates can be calculated by multiplying the force exerted by the distance the crates are moved.
Given that the average force exerted by the mechanical arm is 964 Newtons and the distance is 9.8 meters, we can calculate the work done as:
Work = Force × Distance
Work = 964 N × 9.8 m
Work = 9447.2 Joules
The time it takes to push the crates is given as 23 seconds, so the power can be calculated as:
Power = Work / Time
Power = 9447.2 J / 23 s
Power = 410.747826087 Watts
Therefore, the motor needs to have a power output of at least 410.75 Watts (rounded to two decimal places) to perform this task.