Power Check & Help: 120V Motor, 2.50hp Output, 3hr Operation

  • Thread starter ~christina~
  • Start date
  • Tags
    Power
In summary: If work incresaes then energy increases too. So if I'm not incorrect, I would just solve for W then and that would be the energy transfered?Thus...W=P_e*Ior W=P_e*(1-e)
  • #1
~christina~
Gold Member
714
0

Homework Statement


A 120 V motor has a mechanical power output of 2.50hp It is 90% effiecient in converting power that it takes in by electrical transmission into mechanical power.

a) find current in motor
b) find energy delivered to the motor by electrical transmission in 3.00 h of operation
c) If the electrical company charges $0.160kWh what does it cost to run the motor for 3.00h?

Homework Equations


The Attempt at a Solution



a) find current in motor
[tex]P=I \Delta V[/tex]

and I got

I= 17.08A

b) find energy delivered to the motor by electrical transmission in 3.00 h of operation

would I use this..
[tex]P \Delta t= I \Delta V ( \Delta t ) [/tex] ?

Thanks
 
Physics news on Phys.org
  • #2
a) I got 17.26A. Check for rounding errors.

b) What have you really done by multiplying both sides by [itex]\Delta t[/itex]? Have you done anything?

You are on the right track, but executed wrong. Just remember how power and work are related.

[tex]P=\frac{dW}{dt}= \frac{\Delta W}{\Delta t}[/tex]

Since power has no explicit time dependence we can take derivatives to deltas. Then just remember the work-energy theorem.
 
  • #3
Mindscrape said:
a) I got 17.26A. Check for rounding errors.

I don't get it. It isn't rounding errors. I must have done something wrong in my calculations.
showing what I did, may help:
[tex]P= I \Delta V[/tex]
I think I'm screwing up here when I have to find the power.
I looked up 2.50 horsepower and it was equal to 1864.24968 Watts and
since they said it had 90% efficiency I did this:

[tex]P= \frac{1864.24968W + (1864.24968 W)(.10)} {120V}= 17.08A [/tex]
b) What have you really done by multiplying both sides by [itex]\Delta t[/itex]? Have you done anything?

You are on the right track, but executed wrong. Just remember how power and work are related.

[tex]P=\frac{dW}{dt}= \frac{\Delta W}{\Delta t}[/tex]

Since power has no explicit time dependence we can take derivatives to deltas. Then just remember the work-energy theorem.

If work incresaes then energy increases too. So if I'm not incorrect, I would just solve for W then and that would be the energy transfered?
thus...

[tex]P= \frac{\Delta W} {\Delta t} [/tex]

[tex]\Delta W= P \Delta t = (1864.24968 watts)(3hr)= 5592.74w*hr(3600 J/ 1W*hr) = 20133864 J = 20.133864 MJ [/tex]

I got that but the book has it as 22.4MJ so I'm not sure why I got the above answer.

Thanks
 
Last edited:
  • #4
a) So you know that [itex]P_e = IV[/itex] and that [itex]P_m = .9 P_e[/itex]. So then [itex]P_e = (10/9) P_m[/itex] or [itex](10/9) P_m = IV[/itex]. Solving for I shows that [itex]I= (10/9) P_m/V[/itex]. From here I just used the google calculator to do my conversions.

b) Careful. You forgot to account for the efficiency between the electric motor and the mechanical motor.
 

1. How do you determine the power output of a 120V motor?

The power output of a motor is typically measured in horsepower (hp), and can be calculated by multiplying the voltage (V) by the current (I) in amps. In this case, the power output of a 120V motor can be determined by dividing the motor's wattage by 746 (1 hp = 746 watts).

2. What is the difference between horsepower and watts?

Horsepower (hp) is a unit of power that measures the rate at which work is done, while watts (W) are a unit of power that measures the rate at which energy is transferred. 1 hp is equivalent to 746 watts.

3. How long can a 120V motor with a 2.50hp output operate?

The operating time of a motor depends on various factors such as the load, efficiency, and motor design. However, in general, a 120V motor with a 2.50hp output can operate for approximately 3 hours before needing to cool down.

4. Can a 120V motor with a 2.50hp output be used for heavy-duty tasks?

It depends on the specific motor and its design. Generally, a 120V motor with a 2.50hp output may not be suitable for heavy-duty tasks as it may not have enough power to handle high loads. It is important to check the motor's specifications and recommended usage before attempting to use it for heavy-duty tasks.

5. How can I check if my 120V motor is functioning properly?

There are a few ways to check if a motor is functioning properly, such as checking the voltage and current, inspecting the motor for any damage or wear, and testing the motor under load. It is also important to refer to the manufacturer's instructions and guidelines for proper maintenance and troubleshooting.

Similar threads

  • Introductory Physics Homework Help
Replies
19
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
305
  • Introductory Physics Homework Help
2
Replies
36
Views
5K
  • Introductory Physics Homework Help
Replies
2
Views
664
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Electrical Engineering
Replies
9
Views
604
  • Introductory Physics Homework Help
Replies
3
Views
897
  • Introductory Physics Homework Help
Replies
7
Views
1K
Back
Top