A little help?

dub_dan

1.A person in a wheelchair is moving up a ramp at a constant speed. Their total weight is 900N. The ramp makes an angle of 10degrees with the horizon.
Calculate the force required to keep the wheelchair moving at a constant speed.
(Ignore friction)

2. The ramp is 5m long. Calculate the power exerted by the person in the wheelchair if it takes her 10seconds to travel up the ramp.

Could any1 help me with these?
It's last years physics paper incase it looks familiar.

Sev

Hehe, I think I remember doing this question around June of last year...

1.A person in a wheelchair is moving up a ramp at a constant speed. Their total weight is 900N. The ramp makes an angle of 10degrees with the horizon.
Calculate the force required to keep the wheelchair moving at a constant speed.
(Ignore friction)

I actually found this a difficult concept to get my head around, you have to realise that if the wheelchair was fired up the ramp at 60mph initially, youd still need to exert the same ammount of force to keep it travelling up the ramp at 60mph as you would if it was initially given a velocity of 10mph up the ramp and you were required to sustain that constant velocity of 10mph. Force is mass times acceleration, and acceleration is what changes the velocity of an object.

So to answer this question what you have to do is resolved the forces into components.

The component of force that is normal to the ramp (ie the force that the ramp feels due to the wheelchair is 900N(cos10). But we dont need to worry about this number.

The component of force directed down the ramp is 900N(sin10). And thats our answer to question 1.. you would have to apply that force on the wheelchair up the ramp, to counteract the weight of the wheelchair directed down the ramp.

2. The ramp is 5m long. Calculate the power exerted by the person in the wheelchair if it takes her 10seconds to travel up the ramp.

Power is Work done per second (energy change per second).

Theres two ways you can do this part of the question.

Firstly.. work done by a force is defined as Force x Displacement.
But, Power = Work / Time, so Power = Force x Displacement / Time = Force x Velocity.

Right? so all you do is work out the velocity of the wheelchair up the ramp, and multiply it by the force exerted on the wheelchair.

So the ramp is 5m long, it takes 10 seconds to get up it, so the velocity of the wheelchair up the ramp is 0.5m/sec. Multiply that by the force, and you get power as (0.5)(900N)(Sin10) Joules / sec.

The alternative, but slightly more involved way of doing this question is to work out the total energy that the wheelchair has at the top of ramp = [potential + kinetic energy] = [mgh + (1/2)mv^2] and the total energy that the wheelchair has at the bottom of the ramp = (1/2)mv^2.

(at the bottom of the ramp it has no potential energy, cos its not at a height, it just has kinetic energy because we are assuming that its given an initial velocity, but as you shall see, the actual value of this velocity is inconsequential)

Since the velocity is constant (we are told this in the question), ie, the kinetic energy (1/2mv^2) is constant, you can subtract and see that the total energy change is just 'mgh'. Ie the work done in pushing the wheelchair up the ramp is 'mgh'.

And what is power? work per second, so just divide the work done by the time taken. and you have your answer.

Only glitch in donig it that way is you have to work out h, by inspecting the triangle the ramp makes. h = 5(Sin10)

You also have to work out the mass of the wheelchair, we are only given its weight. But as you know to convert weight in newtons to mass, you just divide by g. (Weight = mg)

So the mass, m, is (900N/g).
The height, h, is 5(Sin10)

And as we worked out, the total energy change from going up the ramp is mgh.

mgh = (900N/g)(g)(5Sin10)

the g's cancel nicely

and we just get (900N)(5Sin10)

To find the work done we just divide that by the time taken = 10 seconds

and we get (900N)(5Sin10)/10 = (0.5)(900N)(Sin10) which is exactly what we got before, and it works out as 78.14 Joules per second. (aka. Watts)

Sev

Theres a diagram of the resolved forces. In case its necessary.



The green arrow being the force you must apply to counteract the component of the weight of the wheelchair down the ramp. Its equal and opposite to the little blue arrow.

Good luck with your mocks (I assume), and in the LC.

dub_dan

Thanks a million for the help Sev!

Sev

No problem.. I didnt mean to bombard you with such a long answer, but I like to give as much detail as possible. And explain every line

Sev

Another thing to clear up, which I should have mentioned, which can be rather confusing, is the idea of work.

Work done on a body is given by force x distance. So if the wheelchair was stationary on the ramp because you were applying a continuous force on the wheelchair to stop it from rolling back down the hill, you would not actually be doing any work on the wheelchair.

The reason being, is that by the definition of work, you are not increasing the wheelchairs total energy. If you stopped pushing the wheelchair and let it roll down the hill, it would still have the same energy.. just some of the potential energy it had from its height on the ramp would be converted to kinetic energy in the form of motion.

But... if you push that wheelchair that extra distance up the ramp.. you are actually increasing its total energy, because it now has extra potential energy because its higher up the ramp. So you have done work on the wheelchair.