Final answer:
The question revolves around calculating the height a motor can lift a 15 kg mass with a 200 W power output in 8 seconds. By converting power to work and equating it to gravitational potential energy, the calculated height is approximately 10.8 meters.
Step-by-step explanation:
The student is asking about the relationship between power, work, and height in the context of a Physics problem related to energy. Given a motor that operates at 200 watts (W), we can determine how high it can lift a 15 kg mass in a time frame of 8.0 seconds.
We know that power (P) is the rate at which work is done, so the work (W) done by the motor in 8.0 seconds is:
W = P × t = 200 W × 8.0 s = 1600 joules (J)
The work done to lift the mass is equal to the gravitational potential energy (GPE) gained by the mass at height (h), therefore:
GPE = m × g × h
Where:
m = mass (15 kg)
g = acceleration due to gravity (9.81 m/s²)
h = height (in meters)
To find the height, rearrange the equation for GPE and solve for h:
h = W / (m × g) = 1600 J / (15 kg × 9.81 m/s²) = 10.8 meters
The motor could lift the 15 kg mass up to a height of approximately 10.8 meters in 8.0 seconds.