Total mechanical work, solving for x

In summary, the conversation is about a problem involving finding x in an equation with multiple variables. The person is struggling to solve for x and has made multiple attempts, but is stuck. They are reminded that it is a quadratic equation and will continue to work on it later.
  • #1
Nano-Passion
1,291
0

Homework Statement



I understand the problem conceptually. I just need help solving for x, which is the hardest part of the problem for me.

1/2mv^2 = 1/2kx^2 + umgx

The Attempt at a Solution



Not really sure how to solve this. I tried and tried to separate by x but nothing worked. Here are 1 of the attempts I suppose. I feel pretty stumped here.

[tex]1/2mv^2 = 1/2kx^2 + umgx[/tex]
[tex]1/2mv^2 - umgx = 1/2kx^2[/tex]
[tex]\frac{mv^2}{k} - \frac{2umgx}{k} = x^2[/tex]
?
 
Physics news on Phys.org
  • #2
Looks like you've got a quadratic equation in x on your hands. Sound familiar?
 
  • #3
gneill said:
Looks like you've got a quadratic equation in x on your hands. Sound familiar?

I thought a lot about how I couldn't expand x^2 + x.. but when you mentioned quadratic equation it came to me right now.. I'll get back to this once I get home.
 

What is total mechanical work?

Total mechanical work refers to the amount of energy that is transferred or transformed in a mechanical system. It takes into account the forces applied and the distance over which they act.

How is total mechanical work calculated?

Total mechanical work can be calculated by multiplying the force applied to an object by the distance over which it acts. This is expressed mathematically as W = F * d, where W is work, F is force, and d is distance.

What are the units of measurement for total mechanical work?

The SI unit for total mechanical work is joules (J), which is equivalent to kg * m^2 / s^2. However, other units such as foot-pounds (ft-lb) or calorie (cal) may also be used in certain contexts.

Why is it important to solve for x in total mechanical work?

Solving for x in total mechanical work allows us to determine the amount of force or distance needed to achieve a certain amount of work. This is useful in practical applications, such as designing machines or calculating the efficiency of a system.

What are some real-world examples of total mechanical work?

Total mechanical work is involved in many everyday activities, such as pushing a cart, lifting weights, or riding a bike. It is also essential in more complex systems, such as engines, turbines, and other mechanical devices.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
863
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
781
  • Introductory Physics Homework Help
Replies
23
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
855
  • Introductory Physics Homework Help
Replies
24
Views
700
  • Introductory Physics Homework Help
Replies
1
Views
751
  • Introductory Physics Homework Help
Replies
8
Views
2K
  • Introductory Physics Homework Help
Replies
20
Views
1K
Back
Top