What is the final velocity of an object sliding down a frictionless ramp?

[Taidhg]

I have a question which asks me if an object with a mass of 2250kg starts from rest at the top of a frictionless ramp 10m long and is at an angle of 10 degrees horizontally, what is the velocity of the object the moment it reaches the bottom of the ramp?
I have been trying to work out this question for hours but it baffles me. It does say It can be calculated using the energy method or the linear motion method but I don't properly understand them.

 

[Dale]

What is the formula for gravitational potential energy and the formula for work?

 

[Taidhg]

What is the formula for gravitational potential energy and the formula for work?

PE = mgh and W = Fd

 

[Dale]

Oops. I meant the formula for gravitational PE and kinetic energy. Sorry.

 

[Taidhg]

Oops. I meant the formula for gravitational PE and kinetic energy. Sorry.

Kinetic energy is 1/2 m v2 but I don't have velocity

 

[Dale]

Kinetic energy is 1/2 m v2 but I don't have velocity

Right, it is what you want to calculate

 

[Taidhg]

Right, it is what you want to calculate

So because GPE = 220725
v2 = 220725-1/2m?

 

[Taidhg]

Right, it is what you want to calculate

my calculations were 220725-½2250 = 219600squared
root 219600 = 468.6 m/s2
I feel like I am doing something wrong.

 

[jtbell]

v2 = 220725-1/2m?

Did you really mean to write 220725 minus 1/2m?

Kinetic energy is 1/2m times v2, not 1/2m plus v2.

By the way, most people here will read 1/2m as "one divided by 2m", not "one-half m". Better to write it as (1/2)m or more simply m/2.

 

[Taidhg]

Did you really mean to write 220725 minus 1/2m?

Kinetic energy is 1/2m times v2, not 1/2m plus v2.

By the way, most people here will read 1/2m as "one divided by 2m", not "one-half m". Better to write it as (1/2)m or more simply m/2.

I see what I have done, I got the right answer at last. Thanks for the help :)

 

[jtbell]

Also, it's a good idea to "first do the algebra, then do the arithmetic." In this case, start with (1/2)mv² = mgh, then rearrange the equation to put v all by itself on the left, and finally plug in the numbers and calculate the result in one go on your calculator. See what happens to m?

 

[Dale]

So because GPE = 220725
v2 = 220725-1/2m?

Where are you getting the $-\frac 1 2 m$? Check your units. Does that make sense? Can you subtract mass from energy?

Always include your units, what you have written is confusing and including units will reduce the confusion and avoid mistakes like this.

 

[sophiecentaur]

my calculations were 220725-½2250 = 219600squared
root 219600 = 468.6 m/s2
I feel like I am doing something wrong.

Stick with the algebraic representation and re-arrangement until the very end and then substitute the numbers that you have. That way you will be able to solve any such question.