Acceleration of mass on an incline plane

In summary: Anyway, your math was wrong in the last step - I'm not sure how you got a value of 6.86. Maybe you input 116.77, as opposed to 166.77?In summary, The force of 100 N pushes a 17 kg block up a frictionless incline making an angle of 31° with the horizontal. The block experiences an acceleration of 6.86 m/s2.
  • #1
gergerger
4
0

Homework Statement



A horizontal force of 100 N pushes a 17 kg block up a frictionless incline that makes an angle of 31° with the horizontal.

Find the acceleration of the block.

Homework Equations



F = ma

F_g = mg

The Attempt at a Solution



Cos31 = 100/(component of force along plane) --> 100/cos31 = F --> F = 166.77N

Then I used this in my F = ma equation producing.

(116.77)N = (17)kg (a)

a = 6.86

This is the wrong answer.
 
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  • #2
gergerger said:

Homework Statement



A horizontal force of 100 N pushes a 17 kg block up a frictionless incline that makes an angle of 31° with the horizontal.

Find the acceleration of the block.

Homework Equations



F = ma

Fg = mg

The Attempt at a Solution



Cos31 = 100/(component of force along plane) --> 100/cos31 = F --> F = 166.77N
the component of the force cannot be greater than the force itself. Recheck that equation.
Then I used this in my F = ma equation producing.

(166.77)N = (17)kg (a)

a = 6.86

This is the wrong answer.
What happened to the component of the weight acting along the plane?
 
  • #3
your second relevant equation is wrong (how can Fg=mg or F=m unless a=1?)

and the first step of the soln is also wrong...
how come component surpasses the force itself?Then solve(without forgetting weight components)...EDIT:: maybe me and phantomjay answered in quite near time gaps!
 
  • #4
@Jay, Firstly, the force was already broken up, so yes the component of the force in the direction of the plane can indeed be bigger than the force in the x direction. I'm not sure what to do about the component of weight, that's rather why I posted the question. You answered nothing.

@Legend. Please, don't post where you have nothing useful to say. It isn't F times g, it's F subg meaning the component of force that is caused by gravity is equal to the mass of an object times acceleration due to gravity. Please, say no more. /facedesk
 
  • #5
Gegerger: First - copping an attitude is not a good way to get help. Second, your initial post was, apparently, not clear - as legend, Jay, and I all seem to have understood the problem in the same manner. Third - your math is simply wrong in the last step - I'm not sure how you got a value of 6.86. Maybe you input 116.77, as opposed to 166.77?
 
  • #6
gergerger said:
@Jay, Firstly, the force was already broken up, so yes the component of the force in the direction of the plane can indeed be bigger than the force in the x direction. I'm not sure what to do about the component of weight, that's rather why I posted the question. You answered nothing.
we don't give answers here, only help, to those who want it.
@Legend. Please, don't post where you have nothing useful to say. It isn't F times g, it's F subg meaning the component of force that is caused by gravity is equal to the mass of an object times acceleration due to gravity. Please, say no more. /facedesk
Chill, you made an error denoting F_g as Fg. So be it. I've done it many times. It happens to the best of us.
 
  • #7
About that help thing... Where is it exactly?

Oh, and whoever said that my math was wrong, it was... sort of. I did use 116.77 in my calculations and that is the right number. I wrote it wrong in the original post. /goes to fix
 
  • #8
gergerger said:
About that help thing... Where is it exactly?

By help, we point you in the right direction. We don't do your work for you.

Now, to clear everything up, please describe the coordinate system you are using so we can all get on the same page.
 
  • #9
gergerger said:
@Jay, Firstly, the force was already broken up, so yes the component of the force in the direction of the plane can indeed be bigger than the force in the x direction. I'm not sure what to do about the component of weight, that's rather why I posted the question. You answered nothing.

@Legend. Please, don't post where you have nothing useful to say. It isn't F times g, it's F subg meaning the component of force that is caused by gravity is equal to the mass of an object times acceleration due to gravity. Please, say no more. /facedesk

Wow... Was going to help you but when I read this I don't want to waste my time. Way to treat the ones that are trying to help you do your freaking homework.
 
  • #10
@Inferior, then why post? Gtfo already. Anyway, I didn't use a coordinate system jhae. If you have a suggestion about how to use one, please explain. ;)
 
  • #11
Perhaps it's time for you to rethink your participation on this forum, gergerger.
 
  • #12
I'm sorry, but did no one realize he had his equation for cosine upside down, or is that what PhanthomJay was trying to imply when he said "recheck that equation"? I just thought it might seem a little more straightforward of an approach to point out his error.

Also, as far as the answer goes, don't forget to include the component of the object's weight acting down the plane when you calculate your net force. The net force should be the difference between the 85.7N push parallel to the incline and the parallel component of the weight (170Nsin31, 87.6N). The block in fact should slide down the incline, with an acceleration 0.11 m/s/s.

The component of the 100N force acting into the plane only increases the normal force and does not cause it to accelerate into the inclined plane. If it were a real incline with friction, however this "perpendicular" component would increase the force of friction as well, which would also be included in your net force. Did that help at all? Are you remembering to turn your head sideways and redefine "horizontal" and "vertical"?
 

Related to Acceleration of mass on an incline plane

1. How does the angle of the incline plane affect the acceleration of a mass?

The angle of the incline plane does not affect the acceleration of a mass. The acceleration of a mass on an incline plane is solely determined by the force of gravity acting on the mass and the mass itself, and is independent of the angle of the incline plane.

2. What is the formula for calculating the acceleration of a mass on an incline plane?

The formula for calculating the acceleration of a mass on an incline plane is a = gsinθ, where a is the acceleration, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the incline plane.

3. How does the mass of the object affect its acceleration on an incline plane?

The mass of the object does not affect its acceleration on an incline plane. The acceleration is solely determined by the force of gravity acting on the mass, and is independent of the mass itself.

4. Can the acceleration of a mass on an incline plane be negative?

Yes, the acceleration of a mass on an incline plane can be negative. This occurs when the incline plane is facing downwards and the force of gravity is pulling the mass in the opposite direction of its motion.

5. How does the friction force on an incline plane affect the acceleration of a mass?

The friction force on an incline plane acts in the opposite direction of the motion of the mass and can decrease its acceleration. The amount of friction force depends on the coefficient of friction between the mass and the surface of the incline plane.

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