Working Like a Horse. 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 1 minute (a) for the average power output you use to lift the crates to equal 0.50 hp; (b) for an average power output of 100 W?
Solution 55E Step 1 of 5: In order to calculate number of crates we can lift in one minute using given power, first we need to calculate the work need to be done in lifting one such crate of mass m= 30 kg to a height h=0.9 m. To calculate work need to be done to lift a crate of mass m= 30kg to a height h=0.9 m Work need to be done against the gravitational potential energy, That is, W c mgh Substituting m= 30 kg, h=0.9 m and g=9.8m/s 2 W c (30 kg)(9.8m/s )(0.9 m) W c 264.6 J Therefore, in order to lift each crate to height h, we need to do a work of 264.6 J . Similarly for n number of crates, W=nW =n c64.6 J Step 2 of 5: (a) for the average power output you use to lift the crates to equal 0.50 hp; Total average power output used to lift n number of crates, P=0.50 hp Using 1hp = 746 W P=373 W Time taken, t= 1 min= 60 sec Total work done in lifting n crates, W=n 264.6 J To find, Number of crates, n= Step 3 of 5: Using average power equation, W P= t Substituting P=373 W, t= 60 sec and W=n 264.6 J n 264.6 J 373 W= 60 sec Solving for number of crates, n = 84.6 per minute Therefore, using the given power we can lift 84.6 crates per minute.