Energy worksheet 5 1 hp 746 w 1 what is the power output of...

Energy: Worksheet 5 (1 hp = 746 W) 1. What is the power output of a motor that can do 4500 J of work every 10.0 s? 2. What power was needed to raise a 14.2 kg object 26.1 m in 5.0 s? What would it be if it was done in 2.5 s? 3. How long would it take a 3000 W machine to raise a 45 kg object 5.5 m? 4. A 60 kg box is lifted by a rope a distance of 10 meters straight up at constant speed. How much power is required to complete this task in 5 seconds? 5. Hulky and Bulky are two workers being considered for a job at the UPS loading dock. Hulky boasts that he can lift a 100 kg box 2.0 meters vertically, in 3.0 seconds. Bulky counters with his claim of lifting a 200 kg box 5.0 meters vertically, in 20 seconds. Which worker has a greater power rating? 6. An 82 kg hiker climbs Mt. Humphrey near Flagstaff. During a two-hour period, the hiker's vertical elevation increases by 540 meters. a. Calculate the climber's ΔUg. b. Find the power generated to increase the hiker's Ug. 7. How long would it take a 7.5 KW motor to raise a 500 kg piano to an apartment window 10 meters above the ground? 8. How much power is required to compress a spring 0.34 m in 0.15 seconds if the spring has a spring constant of 300 N/m? 9. The trains on the Viper are raised from 10 m above ground at the loading platform to a height of 60 m at the top of the first hill in 45 s. Assume that the train (including passengers) has a mass of 2500 kg. Ignoring frictional losses, what power motor (hp) would be required to accomplish this task?

Transcript

00:01 So here you've got a lot of problems on work, energy, and power, particularly around power.

00:08 So i've written down the equations for power, work, and then potential energy for gravity and potential energy of a spring, because those will be helpful in this problem.

00:20 You're also given the conversion between horsepower and watts at the beginning of the problem, which will be helpful in the last part in converting from watts to horsepower, but i didn't write that down.

00:39 So going through the problem, starting with problem one, we know that we've got a work of 4 ,500.

00:52 Jules and that this work can be done in 10 seconds and we want to know what power it's just going to be work divided by time and so in this case that'll be 4 ,500 divided by 10 for a power of 450 watts.

01:14 For problem two we raise a 14 .2 kilogram mass a distance of 26 .1 meters in a time of five seconds.

01:33 So we want to again find the power.

01:37 Power, of course, is work over time, but we're not given the work in this case.

01:43 So we can instead put force times displacement over time.

01:48 And for this problem, that force is going to be force done against the weight of the object if you're lifting it so f should be m g about when you plug all of those things and you get a power of 726 watts to complete it in five seconds we're also asked what if the time is shorter at 2 .5 seconds and in that case again powers going to to be mgd over t, but now you're dividing by 2 .5 instead of 5, and you get a much larger power required of 1 ,453 watts.

02:41 For problem three, it's another power problem, but in this problem we're given that the power is 3 ,000 watts and that that power is used to raise a 45 kilogram mass, a distance of 5 .5 meters, and we want to know how long it's going to take.

03:05 So we're going to use that same equation from above, that power is equal to mgd over t, but we're going to solve for the time.

03:15 And so time is equal to mass, times acceleration due to gravity, times displacement, all divided by the power.

03:23 And when you plug all of those things and you get a time of 0 .8.

03:28 Seconds for problem three.

03:31 I'm going to go back to the top and erase so that we can keep continuing on with the problems.

03:41 So next, excuse me, is number four.

03:46 For number four, now we're considering that a 60 kilogram mass is lifted a distance of 10 meters in a time of five seconds.

04:05 And again, we want to know the power.

04:09 So just like before, power is mgd over t, which when you plug in the specifics of this problem gives you 1 ,176 watts.

04:25 For number five, we're told that hulkie can lift a 100 ,000 ,000 ,000.

04:34 Box, two meters in three seconds.

04:40 And bulky can lift it, can lift a 200 kilogram box, five meters in 20 seconds.

04:49 And we want to know which one is more powerful.

04:53 So again, we're going to find the power of both.

04:56 The power of hulkie will be the 100 kilogram mass times g times.

05:02 Times the distance of two meters, all divided by his time of three, which is equivalent to 653 watts for bulky.

05:19 His power will be the mass of 200 times g, times five meters divided by 20.

05:28 And so we get a power of 490 watts.

05:35 So hulke is our winner.

05:37 He is the more powerful of the two based off of that example anyway...

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