Force and Impulse physics problem

[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.

Homework Statement

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?

Homework Equations

[not sure] ..
mv = Ft ??

The Attempt at a Solution

v = Ft / m = (50N)(4.0s) / (10kg) = 20m/s

Thanks for any help = ) very appreciated

- mandy : )

 

[physixguru]

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

 

[Mandy89]

does it have something to do with

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

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

 

[physixguru]

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

 

[Mandy89]

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

 

[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.

 

[physixguru]

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.

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