Finding Components of Velocity on a Ramp

In summary, the rock slides down a frictionless ice ramp of length L and angle theta to the horizontal. It has an initial velocity of 0. The rock's velocity at the bottom of the ramp is vx=√(2Lgcotθcosθ) and vy=√(2Lgsinθ).
  • #1
Natalie456
16
2
I'm new to this, so I'm sorry if I am doing this process incorrectly. I feel like the answer to this should be straightforward and should just be √(2Lgsinθ). For some reason, I thought there was an acceleration vector along the ramp made up of x and y components, but I don't think this is accurate. My reasoning for this was that the rock is moving in both the negative y and positive x directions, and, since it starts at rest, it will need to accelerate in both of those directions so that it can move in those directions.

1. Homework Statement

A rock is sliding down a frictionless ice ramp of length L and angle theta to the horizontal. It has an initial velocity of 0. You are not allowed to reorient the coordinate plane so that the x-axis is along the ramp. What are the components of the rock's velocity at the bottom of the ramp?

Homework Equations


We aren't allowed to use the work-energy equations or Newton's laws, only kinematics formulas.
Formulas:
1.v=v0+at

2.Δx=v0t + .5at^2

3.v^2=v0^2+2aΔx

The Attempt at a Solution


I think I overcomplicated the problem because of the different axis orientation.

Δy=Lsinθ=.5(g)(t)^2 -- assuming ay=-g
--> time to travel down ramp=√(2Lsinθ/g)
Δx=Lcosθ=.5(ax)(2Lsinθ/g)
ax=gcotθ
vx=√(2Lgcotθcosθ)
vy=√(2Lgsinθ)
 
Last edited:
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  • #2
Welcome to Physics Forums.

Natalie456 said:
time to travel down ramp=√(2Lsinθ/g)
According to this equation, it looks like the smaller the angle, the less time it takes to travel down the ramp. Can that be?
 
  • #3
TomHart said:
Welcome to Physics Forums.According to this equation, it looks like the smaller the angle, the less time it takes to travel down the ramp. Can that be?
I hadn't even thought of that. Do you happen to know how to make sense of this problem using solely kinematics equations? Does the rock have x and y components of acceleration?
 
  • #4
I had a hard time making sense of it. Although I thought that the acceleration along the ramp due to the gravitational force might be equal to gsinθ. Then if you broke that down into x and y components, you would have the x component ax = gsinθcosθ, and the y component ay = gsinθsinθ.
You might try working it that way. You can always check it using the normal way of solving the problem.
 
  • #5
TomHart said:
I had a hard time making sense of it. Although I thought that the acceleration along the ramp due to the gravitational force might be equal to gsinθ. Then if you broke that down into x and y components, you would have the x component ax = gsinθcosθ, and the y component ay = gsinθsinθ.
You might try working it that way. You can always check it using the normal way of solving the problem.
Thanks. I'll give that a shot.
 
  • #6
Natalie456 said:
ay=-g
You mean, it will descend at the same vertical rate as if the ramp were not there?
TomHart said:
the acceleration along the ramp due to the gravitational force might be equal to gsinθ
Quite so, but I am baffled as to how the student is expected to determine that without recourse to Newton's laws. And how else is one to determine the horizontal and vertical components of the acceleration?
 
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Likes Natalie456 and TomHart
  • #7
haruspex said:
You mean, it will descend at the same vertical rate as if the ramp were not there?

Quite so, but I am baffled as to how the student is expected to determine that without recourse to Newton's laws. And how else is one to determine the horizontal and vertical components of the acceleration?
So I would need to use Newton's Laws? I will try using that knowledge, as well. Also, can I state that a=gsinθ along the ramp if the axis for this problem is not to be set along the ramp? Thank you for your time.
 
  • #8
Natalie456 said:
can I state that a=gsinθ along the ramp if the axis for this problem is not to be set along the ramp?
Whether you eventually work in terms of an axis parallel to the ramp or horizontal and vertical axes, at some point you need to establish that the acceleration parallel to the ramp is gsinθ. But I do not see how you can do that without using Newton's laws.
 
  • #9
haruspex said:
Whether you eventually work in terms of an axis parallel to the ramp or horizontal and vertical axes, at some point you need to establish that the acceleration parallel to the ramp is gsinθ. But I do not see how you can do that without using Newton's laws.
Thank you so much! I guess the wording of the problem and my teacher's strictness with regards to the axis threw me off, initially, but now I understand. Thanks, again!
 

Related to Finding Components of Velocity on a Ramp

1. What is acceleration on a ramp?

Acceleration on a ramp is the change in velocity of an object as it moves up or down a sloped surface. It is a measure of how quickly an object's speed is increasing or decreasing.

2. How is acceleration on a ramp calculated?

Acceleration on a ramp is calculated by dividing the change in velocity by the time it takes for that change to occur. This can be represented by the formula: a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. Does the angle of the ramp affect acceleration?

Yes, the angle of the ramp does affect acceleration. The steeper the ramp, the greater the acceleration will be. This is because the steeper the ramp, the more the force of gravity is acting on the object, causing it to accelerate faster.

4. What is the relationship between mass and acceleration on a ramp?

The relationship between mass and acceleration on a ramp is inverse. This means that as the mass of an object increases, the acceleration will decrease. This is because a heavier object requires more force to accelerate it, and the force of gravity remains constant.

5. How does friction affect acceleration on a ramp?

Friction can have a significant impact on acceleration on a ramp. Friction is a force that opposes motion, so it can slow down the acceleration of an object on a ramp. This is why smoother surfaces, with less friction, will result in faster acceleration on a ramp.

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