Intro to Engr Homework. Simple Physic Problem.

[JDM555]

Homework Statement

Assume 50 W of power is used to perform each of the following tasks (one at a time).
a. Lifting 1000kg (1 ton) by one meter.
b. Lifting 1 g (0.001kg) by one meter.
(Hint: What is the potential energy gain by the object?)


How long would it take to complete the first task?
How long would it take to complete the second task?

Homework Equations

PE=mgh
x=1/2at^2+v_0t+x_0 (?)

The Attempt at a Solution

In the hint, it says what is the PE gain by the object. All I know is PE=mgh. In this case m=1000kg, g= 9.8, h=1 meter? Is this correct? If so is it simply 9800? Even if it is 9800, how does that help with finding "How long it would take to complete the task"?

I know I'm solving for T, so a constant acceleration formula that has t but not vfinal is x=1/2at^2+v_0t+x_0. I'm not sure if this is correct though. Does it come to t^2=2/9.8, and you then get the SQRT of that? Or is that completely off?

 

[redargon]

What is the formula for Power in terms of work (energy) and time?

 

[JDM555]

What is the formula for Power in terms of work (energy) and time?

P=W/t

If so, I know power is 50 W correct? Since I want t, would the formula be t= W/p? If so, p= 50, so t= W/50. Now, work, W=Fd? Distance is 1 meter. Force? F=ma? Is this right, or am I running in circles here?

 

[redargon]

you're on the right track and almost there! but you already have the the work... work is energy. The object gains potential energy as it is lifted (work is done during the lifting).

 

[JDM555]

you're on the right track and almost there! but you already have the the work... work is energy. The object gains potential energy as it is lifted (work is done during the lifting).

Oh ok. So hmm, if the object gains PE, I guess that is where the hint comes into place.

PE=mgh correct? m=1000kg, g=9.8, h=1m. Would it just be 9800? t=9800/50=18? 196 seconds?

And for part b, m=0.001kg, g=9.8, h=1m. Would it be 0.0098? t=0.0098/50=0.000196 seconds?

Those numbers don't seem right though. Am I missing something?

 

[redargon]

first off, don't forget your units.

PE=mgh and t=W/P (remember that P is a capital letter for Power, small p is for pressure used in other equations)

a.)
PE=1000*9.81*1 = 9810J (Joules for energy and for work)
That means that 9810J of work is done in lifting the 1ton object 1m (or 9800J depending on how accurate you make your gravity value)
Therefore t=9810/50 = 196 seconds. correct

b.)
PE=0.001*9.81*1 = 0.00981J
That means that 0.00981J of work is done in lifting the 1g object 1m (or 0.0098J depending on how accurate you make your gravity value). This is less work than required to lift 1 ton. This makes sense doesn't it?
Therefore t=0.00981/50 = 0.000196 seconds. correct

I am glad you're asking yourself if those answers make sense. This an important step in every problem. It's a bit difficult to imagine power and energy, because there aren't many references, but we do expect a little motor of 50W to lift 1 ton much slower than to lift 1g, so the answers seem good relative to each other. I think that the answers make sense.

 

[JDM555]

Thank you radargon! I appreciate your help. But there is something else. The next problem says "Although most adults can exert 50W of power, it is clear that neither of the two tasks described in (top problem) can be done by a human. In fact, we have a preferred combination of force and speed at which we can exert the most power. Assume the maximum power we can exert is 100W. What is a reasonable combination of object weight and speed for which you can perform a weight lifting task at 100W power level?

Ehhh...any ideas?