Object slides down frictionless ramp. Find acceleration.

[fergus123]

Homework Statement

Hello, this is my first post here.
I am trying to find acceleration for an object sliding down a ramp. I have the length + height of ramp.

Height: 6.5cm
Length: 130 cm

Homework Equations

I'm at loss here. Vectors are included and this is a kinematics question.

The Attempt at a Solution

Inverse Sin of 6.5/130 give me 2.9 degrees.
Cos(2.9) x 130 is 129.8cm for the horizontal component.

 

[PhanthomJay]

You will have to apply Newton's 2nd law to find the acceleration down the plane as caused by the weight component acting parallel to the incline. See here:
http://hyperphysics.phy-astr.gsu.edu/hbase/mincl.html

 

[fergus123]

Thanks, for the answer, but my question doesn't have mass or friction involved. In elementary level physics.

 

[PhanthomJay]

No friction, fine. But all objects have mass. Make use of the link for the no friction case. Maybe you won't need to know the mass.

 

[Nickie]

Hello, thank you for your question. I would approach this problem by first identifying the forces acting on the object. In this case, since the ramp is frictionless, the only force acting on the object is gravity. We can then use Newton's second law, F=ma, to find the acceleration of the object.

Since the ramp is at an angle, we need to break the force of gravity into its components. The vertical component will be mgcosθ, where θ is the angle of the ramp (2.9 degrees in this case), and the horizontal component will be mgsinθ. The horizontal component is what will cause the object to accelerate down the ramp.

We can then use the equation a=Δv/Δt, where Δv is the change in velocity and Δt is the change in time. In this case, since the object is starting from rest, the initial velocity will be 0. So we can rewrite the equation as a=v/Δt.

To find the final velocity, we can use the equation vf^2=vi^2+2ad, where vf is the final velocity, vi is the initial velocity (0 in this case), a is the acceleration, and d is the distance traveled (130 cm in this case).

Plugging in our values, we get vf^2=0+2a(130 cm). Since we want to find the acceleration, we can rearrange the equation to solve for a: a=vf^2/2d.

Now we just need to find the final velocity, which we can do using the equation vf=vi+at. Since the initial velocity is 0, we can rewrite the equation as vf=at. Plugging in our values, we get vf=a(130 cm)/Δt.

Now we can combine our equations to solve for a:

a=vf^2/2d = [a(130 cm)/Δt]^2/2(130 cm)

Simplifying, we get a= Δt/2.

Therefore, the acceleration of the object sliding down the frictionless ramp is equal to half of the time it takes for the object to travel the length of the ramp. I hope this helps!