What is the speed of block as it reaches O from point P

[Richie Smash]

Homework Statement

A 0.5 Kg block slides from rest down an inclined plane as shown in the figure. The velocity at the bottom of the plane is 6 m/s. The vertical distance PO is 2m.
(gravity = 10m/s²

If the block were to be dropped from P, what would be the velocity at O?

Homework Equations

K.E= (m*v²)/2
P.E= mgh
s= ut + 1/2at²

The Attempt at a Solution

Hi so I figured out the Potential energy at the top which is 10J, and the Kinetic energy at the bottom which is 9J.

I don't know if this will come into play.

I notice that the height is 2 m so I had the speed of when it was falling from P to O i could then calculate everything.

But I don't have the speed, I only have the acceleration due to gravity which is 10 m/s² so from here I'm trying to figure out the time it would take to fall, then I could simply use : (v2-v1)/t

But the problem is I don't have t... I'm trying really hard to figure this out.

I saw I could rearrange the formula for distance in my relevant equations but it seems a bit complicated to single out t from that one, involving completing the square or quadratics, and I honestly truly believe at the level I'm doing (O levels in the Caribbean) they don't want that yet, all I know is that my initial speed is 0 m/s, my distance 2m and my accerleration 10 m/s²

Would someone be so kind to help me?

 

[cnh1995]

A 0.5 Kg block slides from rest down an inclined plane as shown in the figure

As shown in which figure?

 

[gneill]

If the block were to be dropped from P, what would be the velocity at O?

Looks like O is directly below P. Is the whole inclined plane scenario simply an obfuscation?

 

[Richie Smash]

I am not sure if it is an obfuscation, it is from a question from a past practice examination I'm doing... I just am not sure how to calculate the speed of the block if it was dropped from O to P, like I'm pretty sure they mean if it just fell without anything underneath it. They gave the speed of it sliding down the block so I could calculate the kinetic energy at the bottom which was the first part of the question.

 

[gneill]

As given, the problem did not mention if friction acted on the plane, or the angle of the plane. So you have no way to relate the velocity of the sliding block at the bottom of the plane to a block that simply drops vertically without friction. Seems to me that you can only assume that they want the velocity of an object that free-falls vertically from 2 m.

 

[CWatters]

I just am not sure how to calculate the speed of the block if it was dropped from O to P

Revise the equations of motion, there is one that doesn't need t.

 

[CWatters]

I just am not sure how to calculate the speed of the block if it was dropped from O to P

Revise the equations of motion, there is one that doesn't need t.

 

[Richie Smash]

Hi this would be V²=V₀²+2as

So I would get : V²= (0)²+2(10)(2)
V²= 40
V = √40
V=6.32 m/s

 

[haruspex]

Hi this would be V²=V₀²+2as

So I would get : V²= (0)²+2(10)(2)
V²= 40
V = √40
V=6.32 m/s

Yes.
Are there more parts to the question? Maybe one part is to find the coefficient of friction.

 

[kuruman]

Maybe one part is to find the coefficient of friction.

I do not believe there is friction. I think the point of the problem is to compare slide down on a frictionless incline with a straight drop in the absence of air resistance.

 

[Richie Smash]

Yes.
Are there more parts to the question? Maybe one part is to find the coefficient of friction.

Unfortunately no, the only other part of the question says the same thing happens where the block is dropped from P to O except on the moon which has a (g) of 2m/s² and explain whether the velocity at O would be greater or lesser than the value obtained for on earth, which of course it would be lesser because the smaller the acceleration according to the formula V²= V₀²+2as reducing acceleration will clearly reduce it's final velocity.