# Work and Power

### Problems

Problem :

A particle, starting at the origin, experiences a variable force defined by F(x) = 3x 2 , causing it to move along the x-axis. How much work is done on the particle from its starting point to x = 5 ?

Problem :

A 2 kg mass is attached to a spring. The mass is at x = 0 when the spring is relaxed (not compressed or stretched). If the mass gets displaced from the equilibrium point ( x = 0 ) then it experiences a force from the spring described by F s = - kx , where k is a spring constant. The minus sign indicates that the force always points towards the equilibrium point, or away from the displacement of the mass.

From the equilibrium point, the mass on the spring is displaced a distance of 1 meter, then allowed to oscillate on the spring. Using our formula for work from variable forces, and the Work Energy Theorem, find the velocity of the mass when it returns to x = 0 after being initially displaced. let k = 200 N/m .

Initial Displacement of Mass

## Take a Study Break

### Star Trek gets SEXY

Chris Pine and Zoe Saldana heat up the red carpet!

### Are you afraid of relationships?

Auntie SparkNotes can help!

### Sexy starlet style

See every single look from the Met Gala!

### Geeky Actors: Then and Now

Travel back in time!

### Villains We Want These Actresses to Play

From super cute to super bad!

### 10 Movies Better Than Their Books

What do you think?

### How To Look Like J-Law...

When you don't look like J-Law.

### 12 Scientific Inaccuracies in Into Darkness

What did Star Trek get wrong?

## The Book

### Read What You Love, Anywhere You Like

Get Our FREE NOOK Reading Apps