Forces On A Ramp Finding Acceleration Question?

In summary: I just made up the 500N value), the net force on each would give the appropriate, common acceleration.
  • #1
justinh8
44
0
1. Homework Statement
Jane, mass of 55kg holds one end of a vertical rope that passes up over smooth rock and down along a 30 degrees sloping hill as shown. But Josh, mass of 95kg tightly holds the other end of the rope. Assume no friction. Calculate the acceleration. The picture is included
Chatham-Kent-20120327-01002.jpg


The Attempt at a Solution



Fjane = m x g = 55 x 9.81 = 539.5 N
Fjosh = m x g = 95 x 9.81 x sin 30 degrees = 466 N
I know what to do from here but my main question is, will jane go up or will she go down??
According to the forces of gravity jane will go down, right? But the heavier mass belongs to Josh.
If Jane was to get pulled up than the equations would be:

1.T(tension) - mjane(9.81) = mjane x acceleration

2.mjosh x sin(30) - T(tension) = mjosh x acceleration

Is that correct?

if it is i end up with -0.5m/s^2
However, I am not sure if its right please correct me
 
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  • #2
justinh8 said:
1. Homework Statement
Jane, mass of 55kg holds one end of a vertical rope that passes up over smooth rock and down along a 30 degrees sloping hill as shown. But Josh, mass of 95kg tightly holds the other end of the rope. Assume no friction. Calculate the acceleration. The picture is included





Chatham-Kent-20120327-01002.jpg





The Attempt at a Solution



Fjane = m x g = 55 x 9.81 = 539.5 N
Fjosh = m x g = 95 x 9.81 x sin 30 degrees = 466 N
I know what to do from here but my main question is, will jane go up or will she go down??
According to the forces of gravity jane will go down, right? But the heavier mass belongs to Josh.
If Jane was to get pulled up than the equations would be:

1.T(tension) - mjane(9.81) = mjane x acceleration

2.mjosh x sin(30) - T(tension) = mjosh x acceleration

Is that correct?

if it is i end up with -0.5m/s^2
However, I am not sure if its right please correct me


Clearly if Josh was on a level surface, jane would go down, and Josh would go towards the rock.

If the rock was a magic free floating rock, so the the rope to both Josh and Jane was vertical (like over a pulley) Josh would go down, Jane would go up.

Somewhere between the (for Josh) vertical and horizontal extremes they will go no-where - the system will be in balance.

The problem to comtemplate, which side of the balance point is a 30 degree slope.
Your calculated figures are good - and should lead you to a correct decision.
 
  • #3
But in this situation doesn't Jane go down and Josh go up because of the forces

Janes force = 539.5 Newtons
Josh's Force = 466 Newtons

Since Janes force is greater than Joshs force, won't Jane go down and Josh go up??
 
  • #4
justinh8 said:
But in this situation doesn't Jane go down and Josh go up because of the forces

Janes force = 539.5 Newtons
Josh's Force = 466 Newtons

Since Janes force is greater than Joshs force, won't Jane go down and Josh go up??

That is a correct analysis of the situation you presented.
There will be a tension in the rope, the same throughout. It will be an appropriate value between the two forces you have - let's say 500N

At that value the force on Jane are 539.5N down (weight) 500N up (tension) so net force 39.5 Down.
Force on Josh 466N down the slope (weight component) 500N up the slope (tension) so net force 34 N up the slope.

I think you will find that those net forces will give different accelerations for Josh and Jane, which is not possible; they are tied together. BUT if you had the correct tension (I just made up the 500N value), the net force on each would give the appropriate, common acceleration.
 
  • #5
But when you go and solve it won't tension cancel, and initially since tension is the same for both objects wouldn't it be the same answer anyways? Oh and also i would have to divide by the total mass of both Jane and josh right? Or would i just use Jane because it only asks for her VERTICAL acceleration upwards?
 
  • #6
RichardT said:
But when you go and solve it won't tension cancel, and initially since tension is the same for both objects wouldn't it be the same answer anyways? Oh and also i would have to divide by the total mass of both Jane and josh right? Or would i just use Jane because it only asks for her VERTICAL acceleration upwards?

Won't tension cancel with what?

If the tension in the rope was 500N, that means the rope pulls up on Jane with a force of 500N, and pulls along the slope with a force of 500N on Josh. Now a force on Jane is certainly not going to cancel out a force on Josh ?

The tension also means a very complicated force effect on the Rock - but the rock is part of the Earth so the force won't achieve very much due to the ENORMOUS mass of the Earth, so in generally ignored.
 
  • #7
RichardT said:
But when you go and solve it won't tension cancel, and initially since tension is the same for both objects wouldn't it be the same answer anyways? Oh and also i would have to divide by the total mass of both Jane and josh right? Or would i just use Jane because it only asks for her VERTICAL acceleration upwards?

You will need to consider the mass of both when calculating the Tension, if you wish to use Tension during your calculations.
 

FAQ: Forces On A Ramp Finding Acceleration Question?

1. What is a ramp and how does it affect acceleration?

A ramp is an inclined plane that is used to raise objects to a higher level. It affects acceleration by reducing the overall amount of force needed to move an object to a higher position. This is because the ramp allows the force to be spread out over a longer distance, resulting in less work being done.

2. What is the formula for finding acceleration on a ramp?

The formula for finding acceleration on a ramp is a = sin(θ) * g, where a is the acceleration, θ is the angle of the ramp, and g is the acceleration due to gravity (9.8 m/s²).

3. How does the mass of an object affect the acceleration on a ramp?

The mass of an object does not affect the acceleration on a ramp. The acceleration is solely determined by the angle of the ramp and the force of gravity.

4. What is the difference between static and kinetic friction on a ramp?

Static friction is the force that must be overcome to start an object moving on a ramp, while kinetic friction is the force that opposes the motion of the object once it is in motion. On a ramp, static friction is typically greater than kinetic friction.

5. How does the angle of a ramp affect the acceleration of an object?

The angle of a ramp directly affects the acceleration of an object. As the angle increases, the acceleration also increases. This is because a steeper angle means that the force of gravity is acting more directly on the object, resulting in a greater acceleration.

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