• Sep 5th 2011, 01:28 AM
furor celtica
A winch is used to raise a 200 kg load. The maximum power of the winch is 5 kW. Calculate the greatest possible acceleration of the load when its speed is 2 ms^1, and the greatest speed at which the load can be raised.

Alright so this is how I went about things: power=force x velocity, so upward force = 5000/2 = 2500. So net upward force = 500 N, so greatest possible acceleration = 500/200 = 2.5 ms^2.
I know this is incorrect, where did I go wrong?
• Sep 5th 2011, 04:49 AM
skeeter
Quote:

Originally Posted by furor celtica
A winch is used to raise a 200 kg load. The maximum power of the winch is 5 kW. Calculate the greatest possible acceleration of the load when its speed is 2 ms^1, and the greatest speed at which the load can be raised.

Alright so this is how I went about things: power=force x velocity, so upward force = 5000/2 = 2500. So net upward force = 500 N, so greatest possible acceleration = 500/200 = 2.5 ms^2.
I know this is incorrect, where did I go wrong?

$\displaystyle P = F \cdot v = ma \cdot v$

$\displaystyle a = \frac{P}{mv} = \frac{5000}{200(2)} = 12.5 \, m/s^2$
• Sep 5th 2011, 06:21 AM
furor celtica
thanks for your time bud, but the correct answer is 0.2 ms^2
• Sep 5th 2011, 06:34 AM
skeeter
Quote:

Originally Posted by furor celtica
thanks for your time bud, but the correct answer is 0.2 ms^2

yes, I forgot to take the work done by the force of gravity ... but taking that into account, I arrive at 2.5 m/s^2 also.
• Sep 6th 2011, 07:49 AM
furor celtica
well that doesnt help me then does it
• Sep 11th 2011, 09:48 PM
furor celtica
alrighty now i've got an issue with ths second problem, finding the greatest speed at which the load can be raised
so greatest speed means the upwards force is equal to the downwards force, so the upwards force will be 2000N
power being 5000, speed is 2.5 ms^1
however the answer is 2.55, another typo or did i truly get it wrong this time?
• Sep 11th 2011, 11:44 PM
CaptainBlack
Quote:

Originally Posted by furor celtica
A winch is used to raise a 200 kg load. The maximum power of the winch is 5 kW. Calculate the greatest possible acceleration of the load when its speed is 2 ms^1, and the greatest speed at which the load can be raised.

Alright so this is how I went about things: power=force x velocity, so upward force = 5000/2 = 2500. So net upward force = 500 N, so greatest possible acceleration = 500/200 = 2.5 ms^2.
I know this is incorrect, where did I go wrong?

$\displaystyle f= mg+m\dot{v}$

$\displaystyle \text{power}=\text{rate of doing work}=fv= (mg+m\dot{v})v$

which to me looks like $\displaystyle \dot{v}=2.5 \text{ m/s}^2$.

Consider the possibility that the known correct answer is wrong?

CB
• Sep 11th 2011, 11:48 PM
CaptainBlack
I agree with you, you set $\displaystyle \dot{v}=0$ and solve for $\displaystyle v$ that gives $\displaystyle 2.5 \text{ m/s}$