# Homework Help: Find Work of a Force Acted on Mass over Frictionless Surface

1. Sep 25, 2011

### mrsteve

1. The problem statement, all variables and given/known data
A force given by $$F(x)=5x^3 (in \frac {N}{m^3})$$ acts on a 1-kg mass moving on a frictionless surface. The mass moves from x = 2m to x = 6m.

a) How much work is done by the force?

2. Relevant equations

$$W=\int F_x from x_o to x_f$$

3. The attempt at a solution

$$\int 5x^3 from x=2 to x=6 = 1.6*10^3$$

Is this correct?

2. Sep 25, 2011

### Ignea_unda

Looks correct to me, mrsteve.

3. Sep 25, 2011

### mrsteve

Also, if the speed of the mass is 2 m/s @ x=2 what is the speed at x=6?

$$KE=\frac{mv^2}{2}$$

$$1600=\frac{(1)(v^2)}{2} => v=5.6*10^1 = 60 m/s$$

Would that be correct?

4. Sep 25, 2011

### mrsteve

The book has 2,000 J. I suppose that's because there's only 1 significant digit in mass = 1kg?

$$1.6 *10^3 => 2 *10^3$$