Solve KE, PE and Work for Block Sliding Down Friction-Less Incline

[zzoo4]

Homework Statement

How do you solve this??

A 2kg block starts from rest slides down a friction-less incline plane that is at angle of 20degree with the horizontal. At a certain point on the incline, the speed of the block is 9m/s.

1.What is the vertical distance the block has traveled??
2.What is the work done by gravity as the block moves the vertical distance you found??

Homework Equations

Work= Force x Displacement
KE= .5mv^2
PE= mgh

The Attempt at a Solution

for number 1, I know that my PEf nd KEi =0.
So i set PEi and KEf equal to each other.
PEi=KEf.
So what i did was mgh=.5*m*v^2.
m's cancel out.

so 9.8h=.5v^2.
.. This is where i am stuck.. I am not sure if i am doing right.. But how do i find v which is velocity?

 

[SammyS]

I think it gives the velocity in the problem statement. (actually the speed)

 

[zzoo4]

Then how do i solve it?

 

[SammyS]

...

for number 1, I know that my PEf nd KEi =0.
So i set PEi and KEf equal to each other.
PEi=KEf.
So what i did was mgh=.5*m*v^2.
m's cancel out.

so 9.8h=.5v^2.
.. This is where i am stuck.. I am not sure if i am doing right.. But how do i find v which is velocity?

Solve your last equation for h.

 

[zzoo4]

I cant..

 

[zzoo4]

O~ do i just substitute 9??

 

[SammyS]

You should be able to solve it. What is v ?

 

[zzoo4]

the speed is 9.. Okay i got #1 which is 4.14 m..

But cannot find the work done by gravity??

 

[SammyS]

What's the force of gravity, on the block?

 

[zzoo4]

39.24

 

[zzoo4]

Is this right??

W= 39.24 * 4.13cos(30).

= 140??

 

[zzoo4]

in joules??

 

[zzoo4]

Or is it Pe=mgh??

4kg*9.8*4.13= 161J?

 

[SammyS]

Why 4 kg ?

(2kg )(9.8 N/kg) = ?

The weight!

 

[zzoo4]

Oh sorry. I thought the mass was 4kg.
so its actually.

2kg * 9.8 n/kg = 19.6 N.

So what now??

 

[SammyS]

Work= Force x Displacement (sort of)

Actually: Work= Force x (the component of Displacement that's in the direction of the force)

the component of Displacement that's in the direction of the force = h

 

[zzoo4]

so its.

W=19.6 N * 4.13cos(20)?

 

[zzoo4]

or is it sin(20)??