# Force and Impulse

1. Feb 24, 2008

### Mandy89

I attempted the qn .. but I'm not sure if this is the correct way of going about it..
the relevant equations used weren't given.

1. The problem statement, all variables and given/known data
Force and Impulse:

The magnitude of an unbalanced force on a 10 kg object increases at a constant rate from 0N to 50N in 4.0s, causing the initially stationary object to move.

What is the speed of the object at the end of the 4.0s?

2. Relevant equations
[not sure] ..
mv = Ft ??

3. The attempt at a solution
v = Ft / m = (50N)(4.0s) / (10kg) = 20m/s

Thanks for any help = ) very appreciated

- mandy : )

2. Feb 25, 2008

### physixguru

This would involve integration...since the force is UNBALANCED.
Do you have any concept regarding it?

3. Feb 25, 2008

### Mandy89

does it have something to do with

F = ma = m(dv/dt) ??

= S .. i honestly have no idea what to do with it

4. Feb 25, 2008

### physixguru

yupp and intergral from the given displacement.
if ya want the concept reply for it.

5. Feb 25, 2008

### Mandy89

yes could i please have the concept ..
thanks for your help : )

6. Feb 25, 2008

### Tedjn

The simple way to do this problem is to recognize that if the force increases by a constant rate, you can simply use the average of the initial and final forces as the average force applied for the entire time. In your example, the average force would be 25 N applied for 4 seconds, giving you an impulse of 100 kg m/s

You can see why you can use 25 N as the average force if you actually do out the integration. What you have is

$$F = ma = m\frac{dv}{dt} \implies F dt = m dv \implies \int_{t_a}^{t_b} F dt = \int_{v_a}^{v_b} m dv = mv_b$$

because $v_a = 0$.

Now, what is the force F? Remember that it increases at a constant rate from 0 to 50 N in 4 seconds. Since it increases at a constant rate, F must be linear.

Last edited: Feb 25, 2008
7. Feb 26, 2008

### physixguru

first of all let him have a concept of integration and differentiation.