Calculating Pressure: Force, Mass, Acceleration

[parwana]

The combustion reaction of gasoline vapor in an automobile cylinder accelerates the piston at 2024.0 cm/s2. The piston has a mass of 500.0 g and a diameter of 5.50 cm.

Calculate the pressure in Pascals exerted on the piston by the expanding gases in the cylinder.

Remember from Newton's Law in Physics that force = mass times acceleration.

 

[mrjeffy321]

I just assume this is how to solve it,

m = .5 kg
a = 20.24 m/s^2
F = m*a
F = .5 * 20.24 = 10.12 N which is equal to the force of the weight of 1.03 kg

Diameter of piston is 5.5 cm = .055 m
r = .0275 m
area = pi*r^2
area = 3.1415 * (.0275^2) = .0024 square meters.

so you have the force of 1.03 kg exerted on an area of .0024 sqaure meters,
then we can convert this into more usable forms, like pounds per square inch.
1.03 kg = 2.27 pounds
.0024 square meters = 3.72 square inches
so pounds per square inch (psi) is equal to = .61
then we convert this into pascals, .61 psi = 4206 pascals

there is probable a better way to do this, I am not even saying this is right, but it seems like the logical thing to do to me.

 

[parwana]

thats wrong, i tried that too without converting to square inches and such

 

[Gokul43201]

parwana, the policy here is that we can not help you unless you tell us what you've tried.

mrjeffy's been more helpful than he should. However, in this case, it looks like you have attempted the problem (in the manner that mrjeffy has, above). We need to know that there's been an effort made before coming here.

So, in this problem, what you likely forgot to consider is that there is 1 atmosphere of pressure acting on the other side of the piston.

 

[parwana]

what would that mean though, see the problem here is that our professor assigns us these problems, when we haven't even covered them yet in the class, i need major help with this

well what i thought of doing was

mass times acceleration gives you the force

then force divided by the area(3.14x(2.25x2.25))

i didnt get it right though

 

[mrjeffy321]

well, using F=m*a, that will actually give you the net force acting on the object. Gokul43201 pointed out that there is 1 atmosphere of pressure acting in the opposite direction of the motion (we'll call the direction of motion "down", and opposite the direction of motion "up").
Net Force = Force Down - Force Up
so, if in theory, I was on the right track before, then that would be your net force, and you know the force up, so you can solve for the force down, this is however assuming I was on the right track all along, which I am not sure that I was.

 

[Gokul43201]

jeff (if I may call you that) : your apprach (and parwana's) is correct.

parwana : F = ma gives you the net force, as explained above. Now if you draw a free-body diagram for the piston, it tells you that the net force = force from gas - force due to atmosphere.

So, force from gas, F(gas) = F(net) + F(atm) = ma + F(atm)
Dividing this by the area, A, you get, P(gas) = (ma/A) + P(atm).

You have already calculated the first term on the RHS. You only need to add P(atm) = about 100,000 Pa to this, to get the required answer.

 

[parwana]

ok this is what i did
mass x acceleration= 10.12 N + 1 atm= 11.12

11.12/.0024= 4633.3, now what??

 

[Gokul43201]

ok this is what i did
mass x acceleration= 10.12 N + 1 atm= 11.12

11.12/.0024= 4633.3, now what??

This is wrong. You can not add a force and a pressure. And when you add two forces, you have to make sure they have the same units. Please read my above post.

 

[parwana]

please can u do the problem and explain at each step?

 

[mrjeffy321]

what you did wrong is that you added a force and a pressure together, you can't do that, they describe different things.
you need you convert one of them to the other in order to add them.

What I would do is find the pressure that would be equal to the net force acting on the piston (10.12 N = ?), find that answer in atmospheres of pressure to make it easier, then just add one atmosphere to get the total pressure, then convert that into pascals for your final answer.

 

[parwana]

how do i do that though, we haven't covered this yet and our professor assigns us gthese problems in advance, please can u do it and explain it step by step

 

[Gokul43201]

parwana, I've done it for you (step by step) in post #7. You just have to plug in numbers into the final expression.

 

[parwana]

jeff (if I may call you that) : your apprach (and parwana's) is correct.

parwana : F = ma gives you the net force, as explained above. Now if you draw a free-body diagram for the piston, it tells you that the net force = force from gas - force due to atmosphere.

So, force from gas, F(gas) = F(net) + F(atm) = ma + F(atm)
Dividing this by the area, A, you get, P(gas) = (ma/A) + P(atm).

You have already calculated the first term on the RHS. You only need to add P(atm) = about 100,000 Pa to this, to get the required answer.

so its mass divided by area, plus 100000??

please help

its .500/.0024, plus 100000?

 

[Gokul43201]

Either you forgot about the acceleration, 'a', or you haven't heard of Newton's Second Law, F(net) = ma.

I hope it was just the former - a careless error. Look at the equation again, and understand how it works, rather than just trying to get the answer by the quickest route.

 

[parwana]

its ok gokul and jeff thanks for your help, i finally figured it out.

i did F=ma

foudn the force as 10.12

then i got area as .00237

then i did Pressure= force/area
10.12/.00237

and got 4261 pascals

 

[Gokul43201]

Unfortunately, this is the wrong answer. The correct answer should be 1.04 kPa.

 

[mrjeffy321]

again, you just found the net force there, and from that, you found the net pressure you need to remember to add the atmspheric pressure to your answer.

knowing now that a pascal of pressure is defined as Newtons/m^2, that makes this problem considerably simpler. I was taking the LONG way when I converted the force to psi and then psi to pascals.