An electrical motor provides 0.50W of mechanical power. How much time will it take motor to lift a 0.1 kg mass at constant speed form to a shelf 2.0 m above the floor?
a. 0.25s
b. 0.40s
c. 1.0s
d. 4.0s
The Correct Answer and Explanation is :
To solve the problem of how long it takes for an electric motor to lift a 0.1 kg mass to a height of 2.0 m at a constant speed with a power output of 0.50 W, we can use the relationship between power, work, and time.
Step 1: Calculate the Work Done
The work done (W) against gravity to lift the mass can be calculated using the formula:
[
W = m \cdot g \cdot h
]
Where:
- ( m ) is the mass (0.1 kg),
- ( g ) is the acceleration due to gravity (approximately 9.81 m/s²),
- ( h ) is the height (2.0 m).
Substituting the values:
[
W = 0.1 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 \cdot 2.0 \, \text{m} = 1.962 \, \text{J}
]
Step 2: Relate Power to Work Done
Power (P) is defined as the rate at which work is done, given by the formula:
[
P = \frac{W}{t}
]
Where:
- ( P ) is the power (0.50 W),
- ( W ) is the work done (1.962 J),
- ( t ) is the time in seconds.
Step 3: Rearrange the Equation to Solve for Time
Rearranging the power formula gives us:
[
t = \frac{W}{P}
]
Substituting in our values:
[
t = \frac{1.962 \, \text{J}}{0.50 \, \text{W}} = 3.924 \, \text{s}
]
Conclusion
This means it will take approximately 3.924 seconds to lift the 0.1 kg mass to a height of 2.0 m at constant speed with a power output of 0.50 W.
Answer
Given the options:
- a. 0.25s
- b. 0.40s
- c. 1.0s
- d. 4.0s
The closest correct answer is d. 4.0s.