A student tries to lift an 85 pound rock at the end of 10 seconds the rock is not moved how much work was done on the rock if it took him 1.4 seconds to lift the rock how much power P equals E/T was needed? Later he tries again and lifts the rock to a height of 4.2 feet. how much work was done? How many horsepower were needed?
We can calculate the work done on the rock using the formula:
Work = Force × Distance × cos(θ)
Where:
- Force is the force applied to lift the rock
- Distance is the distance the rock is lifted
- cos(θ) is the cosine of the angle between the applied force and the displacement (assumed to be 0°, as the force is applied vertically)
For the first part, when the rock is not moved, the work done is 0 since no distance is covered.
For the second part, where the student lifts the rock to a height of 4.2 feet, we need to convert the distance to the corresponding units. Since 1 foot is approximately equal to 0.3048 meters, we have:
Distance = 4.2 feet × 0.3048 meters/foot = 1.28016 meters
Considering the weight (85 pounds) as the force applied, we need to convert it to Newtons. Since 1 pound is equal to 4.44822 Newtons, we have:
Force = 85 pounds × 4.44822 Newtons/pound = 377.9977 Newtons
Now, we can calculate the work done:
Work = 377.9977 Newtons × 1.28016 meters × cos(0°) = 377.9977 Joules
To calculate the power required (P = E/T), we need the time (T). However, the time given (1.4 seconds) is for lifting the rock, not for the entire process. So, we cannot find the power without the total time required.
Lastly, to calculate the horsepower needed, we can use the conversion factor that 1 horsepower is equal to 746 watts. Therefore:
Horsepower = Power (in watts) / 746
Since we couldn't find the power in the previous calculation, we cannot determine the horsepower needed.