Box sliding down frictionless incline

In summary: Great job on using conservation of energy to solve this problem. In summary, the box initially at rest at the top of a frictionless ramp is allowed to slide to the bottom. Its speed at the bottom is 4 m/s. When the box is slid down the ramp a second time with an initial speed of 3 m/s, its speed at the bottom is 4.9 m/s, using conservation of energy.
  • #1
pewpew23
15
0

Homework Statement



A box initially at rest at the top of a frictionless ramp is allowed to slide to the bottom. At the bottom its speed is 4 m/s. Next, the box is again slid down the ramp, but this time it does not start from rest. It has an initial speed of 3 m/s at the top. How fast is it going when it gets to the bottom?

Homework Equations



No idea...


The Attempt at a Solution



Since the length of the ramp, mass of the block, nor the time it takes to get from the top of the ramp to the bottom is given... I don't know where to start with this one.
 
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  • #2
EDIT: What I had done was wrong :).

Matterwave is correct, just use conservation of energy.
 
Last edited:
  • #3
I'm not sure I understand your equation...
vf meaning velocity and ?
vi is initial velocity, correct?
 
  • #4
I'm not sure I understand your equation...
vf meaning velocity and ?
vi is initial velocity, correct?

Yes, I'm just using a subscript to denote the initial and final states of the velocity.
 
  • #5
Perhaps Jegues' method is simpler, but I would approach this in terms of energy conservation. Potential energy at top = kinetic energy at bottom. The m's will cancel out.
 
  • #6
so a=(vf-vi)/t

a=4/t

a=(vf-3)/t

set them equal to each other
4/t = vf-3/t

t's cancel out and we get 4= vf-3
and vf=7 :)
 
  • #7
Bump, I edited my post above. As Matterwave suggested conservation of energy is what you're looking for.

EDIT:
so a=(vf-vi)/t

a=4/t

a=(vf-3)/t

set them equal to each other
4/t = vf-3/t

t's cancel out and we get 4= vf-3
and vf=7 :)

This is what I had initially suggested. It is wrong. Use conservation of energy, sorry in advance for any confusion.
 
  • #8
KE= 1/2mv^2
GPE= mgh

and that would give us h= .81716
but how would I use that solve for vf is vi=3?
 
  • #9
You generated the height using the first case good!

Now for second case, in the intial state what types of energy are there? In the final state what types of energy are there?
 
  • #10
At the top of the ramp, all energy is in Gravitational Potential (mgh) and KE.
and at the bottom there is only KE.

1/2vi^2 + gh = 1/2vf^2
12.499 = 1/2vf^2
and vf = 4.9
 
  • #11
Looks correct to me!
 

FAQ: Box sliding down frictionless incline

What is a frictionless incline?

A frictionless incline is a hypothetical surface that has no resistance to motion. This means that any object sliding down the incline will not experience any frictional force, allowing it to accelerate down the incline without any external interference.

How does the angle of the incline affect the motion of the box?

The angle of the incline will determine the acceleration of the box. The steeper the incline, the greater the acceleration of the box. This is because the force of gravity acting on the box is split into two components: one parallel to the incline and one perpendicular to the incline. As the incline angle increases, the parallel component of gravity increases, resulting in a greater acceleration of the box.

What is the equation for calculating the acceleration of the box on a frictionless incline?

The equation for calculating the acceleration of the box on a frictionless incline is a = sin(θ) * g, where θ is the angle of the incline and g is the acceleration due to gravity (9.8 m/s^2). This equation assumes that the incline is smooth and the box is not rotating as it slides down.

Can a box ever reach a constant speed while sliding down a frictionless incline?

No, a box cannot reach a constant speed while sliding down a frictionless incline. This is because there is no force acting on the box to counteract its acceleration due to gravity. Therefore, the box will continue to accelerate until it reaches the bottom of the incline or encounters another force, such as air resistance.

How does the mass of the box affect its acceleration on a frictionless incline?

The mass of the box does not affect its acceleration on a frictionless incline. This is because, in the absence of friction, all objects will accelerate at the same rate regardless of their mass. This is known as the principle of equivalence, which is a fundamental principle in physics.

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