Your job is to lift 30-kg crates a vertical distance of 0.90 m from the ground onto the bed of a truck. How many crates would you have to load onto the truck in one minute for the average power output you use to lift the crates to equal 0.50 hp?

To determine how many 30-kg crates you need to lift in one minute to achieve an average power output of 0.50 horsepower (hp), we first need to understand the relationship between work, power, and time. Power is defined as the rate at which work is done, and it can be calculated using the formula:

Understanding Work and Power

Work is the product of force and distance. In this case, the force required to lift each crate is equal to its weight, which can be calculated using the formula:

• Weight (Force) = mass × gravitational acceleration

Here, the mass of each crate is 30 kg, and the gravitational acceleration is approximately 9.81 m/s². Therefore, the weight of one crate is:

• Weight = 30 kg × 9.81 m/s² = 294.3 N

Calculating Work Done

Next, we calculate the work done in lifting one crate a vertical distance of 0.90 m:

• Work = Force × Distance

Substituting the values we have:

• Work = 294.3 N × 0.90 m = 264.87 J (joules)

Power Output Calculation

Now, we need to convert the desired power output from horsepower to watts, since 1 hp is equivalent to approximately 746 watts. Therefore, 0.50 hp is:

• 0.50 hp × 746 W/hp = 373 W

Power can also be expressed as work done per unit time:

• Power = Work / Time

We want to find out how many crates we can lift in one minute (60 seconds) to achieve this power output. Rearranging the formula gives us:

• Work = Power × Time

Substituting the values we have:

• Work = 373 W × 60 s = 22,380 J

Finding the Number of Crates

Now, to find out how many crates you can lift to equal this amount of work, we divide the total work by the work done per crate:

• Number of crates = Total Work / Work per crate

Substituting the values:

• Number of crates = 22,380 J / 264.87 J/crate ≈ 84.5

Since you can't lift a fraction of a crate, you would need to round down to the nearest whole number. Therefore, you can lift a maximum of 84 crates in one minute to achieve an average power output of 0.50 hp.

Summary

In summary, to match a power output of 0.50 hp while lifting 30-kg crates a distance of 0.90 m, you would need to load approximately 84 crates onto the truck in one minute. This calculation illustrates the relationship between force, work, and power, and how they interact in practical scenarios like lifting heavy objects.