# Solved it Nope. - Piano slipping down a ramp

• Medgirl314
In summary, the piano takes 2.03 seconds to roll down the ramp. The mass doesn't affect the time taken.
Medgirl314
Solved it! Nope. -- Piano slipping down a ramp

## Homework Statement

Two men loading a 900 kg piano onto a truck lose control and the piano slips, rolling down the loading ramp. The ramp is a 12 degree incline that is 3.2 m long. How long does it take the piano to reach the bottom of the ramp? Assume there is no friction.

## Homework Equations

My physics teacher found this equation for acceleration for an object on an incline:
a=g(sin)(theta)-(mu)g(cos)(theta)

I tried tweaking it a bit. I think the (mu)g(cos) can be left out since mu is zero.

a=g(sin)theta
a=9.8(.20)
a=2.03 m/s^2

Easy, right?

## The Attempt at a Solution

Nope. Not easy. The equation I found above doesn't take mass into consideration. Using this acceleration as my change in velocity, I get t=2.03/3.2=0.63 s. Reasonable enough. But what about the mass? Where did I go wrong?

Not good. Acceleration is change in velocity. You've learned other expressions for linear motion with constant acceleration. List a few under 2..

And: acceleration/length is not the dimension of time !
Also: ##\sin \left( \frac {12}{180}\pi\right) = 0.2## is a bit coarse

1 person
Medgirl314 said:

## Homework Statement

Two men loading a 900 kg piano onto a truck lose control and the piano slips, rolling down the loading ramp. The ramp is a 12 degree incline that is 3.2 m long. How long does it take the piano to reach the bottom of the ramp? Assume there is no friction.

## Homework Equations

My physics teacher found this equation for acceleration for an object on an incline:
a=g(sin)(theta)-(mu)g(cos)(theta)

I tried tweaking it a bit. I think the (mu)g(cos) can be left out since mu is zero.

a=g(sin)theta
a=9.8(.20)
a=2.03 m/s^2

Easy, right?

## The Attempt at a Solution

Nope. Not easy. The equation I found above doesn't take mass into consideration. Using this acceleration as my change in velocity, I get t=2.03/3.2=0.63 s. Reasonable enough. But what about the mass? Where did I go wrong?

Your value for the time taken is incorrect.

You know that ##a=2.03 ms^{-2}##. You know that it travels a distance ##s=3.2 m##. We also know that the piano's initial speed is zero, so ##u=0 ms^{-2}##.

You want to find the time taken, ##t##.

Do you know a formula that connects ##s##, ##u##, ##a## and ##t##?

1 person
Yeah, I didn't think so, but there have been certain instances where the acceleration was the velocity, so I figured there was no harm in playing with it.

a=Δv/Δt
x=x0+v0t+1/2at^2
v^2=v0^2+2aΔx

Hm. Would the last one work? If so, why don't I need to account for the mass?

Rococo said:

Your value for the time taken is incorrect.

You know that ##a=2.03 ms^{-2}##. You know that it travels a distance ##s=3.2 m##. We also know that the piano's initial speed is zero, so ##u=0 ms^{-2}##.

You want to find the time taken, ##t##.

Do you know a formula that connects ##s##, ##u##, ##a## and ##t##?

What's ##u## ? I think we may have different variables for that quantity.

Medgirl314 said:
Yeah, I didn't think so, but there have been certain instances where the acceleration was the velocity, so I figured there was no harm in playing with it.

a=Δv/Δt
x=x0+v0t+1/2at^2
v^2=v0^2+2aΔx

Hm. Would the last one work? If so, why don't I need to account for the mass?

You are trying to find the time taken, ##t##. Therefore the equation you choose must have ##t## in it.

The middle equation is the one you need. Using the symbols I used in my previous post, the equation can be written:

##s=ut + \frac{1}{2}at^{2}##

If you were to place a golf ball and a bowling ball at the top of the ramp, they would both roll down, and reach the bottom of the ramp at exactly the same time. This might seem surprising, but the time taken for an object to roll down the ramp does not depend on the mass of the object. The acceleration for any object will be the same, ##a=gsinθ## , as you correctly showed.

Medgirl314 said:
What's ##u## ? I think we may have different variables for that quantity.

Yes, I usually use the symbol ##u## to mean the initial velocity of the object. It is the same thing as ##v_0##.

Sorry, I mis-stated my question about the mass. I understand that the time doesn't depend on the mass, but I was wondering why it was included in this problem. Just to throw me off? It worked. ;-)

s=ut+1/2 at^2
s=1/2at^2

Major brain lapse. When we say at^2, do we mean just the t is squared?

Thanks again!

Medgirl314 said:
Sorry, I mis-stated my question about the mass. I understand that the time doesn't depend on the mass, but I was wondering why it was included in this problem. Just to throw me off? It worked. ;-)

s=ut+1/2 at^2
s=1/2at^2

Major brain lapse. When we say at^2, do we mean just the t is squared?

Thanks again!

Yes, the mass of piano is not needed to solve the problem.

Yes, just the t is squared: ##\frac{1}{2}at^2=\frac{1}{2} \times a \times t \times t##

So, you have the correct equation:

##s=\frac{1}{2}at^2##

You know that ##s=3.2m## and ##a=2.03 ms^{-2}##.

Can you now use the equation to find ##t##?

1 person
s/a=1/2t^2
3.2/2.03=1/2t^2
1.57=1/2t^2
3.14=t^2
1.77=t.

Okay, that may not be right. But I really, really, really want it to be because pi.

Medgirl314 said:
s/a=1/2t^2
3.2/2.03=1/2t^2
1.57=1/2t^2
3.14=t^2
1.77=t.

Okay, that may not be right. But I really, really, really want it to be because pi.

Yes, that's correct.

1 person
Yay! My physics teacher is epic. Thank you!

See, some physicists are not too bad... almost human

1 person

## What is "Solved it Nope. - Piano slipping down a ramp"?

"Solved it Nope. - Piano slipping down a ramp" is a phrase that describes a physics problem in which a piano is placed on a ramp and allowed to slide down. The goal is to determine the factors that affect the speed and acceleration of the piano as it slides.

## What are the main factors that affect the speed and acceleration of the piano?

The main factors that affect the speed and acceleration of the piano are the angle of the ramp, the weight of the piano, and the friction between the piano and the ramp.

## How does the angle of the ramp affect the piano's speed and acceleration?

The steeper the angle of the ramp, the faster the piano will accelerate and the higher its speed will be. This is because a steeper ramp provides a greater force of gravity pulling the piano down the ramp.

## What role does the weight of the piano play in this problem?

The weight of the piano affects the amount of force needed to move it down the ramp. A heavier piano will require more force to accelerate and reach a higher speed compared to a lighter piano.

## How does friction affect the piano's movement down the ramp?

Friction between the piano and the ramp will slow down the piano's movement. The higher the friction, the more force will be needed to overcome it and maintain the piano's speed. Factors that can affect friction include the material of the ramp and the surface of the piano.

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