Deriving Speed at an Inclined Plane

[zcabral]

Homework Statement

A block slides down a frictionless plane having an inclination of = 12.2° (Fig P5.22). The block starts from rest at the top and the length of the incline is 2.85 m.

Homework Equations

F=ma
xf=xi+vit+1/2at^2

The Attempt at a Solution

i tried to solve this by using the kinematic equation above. i know the acceleration is 2.07 m/s^2 so i plugged it into find t in order to find speed but it didnt work. I am totally stuck. i know if i find t i could find the answer by absolute value v=dx/dt

 

[dabig2]

If you're searching for the velocity of the block at the very bottom of the ramp, you actually utilize Energy conservation instead of kinematics.

PE = mgh
KE = 1/2*mv^2

The block is at rest on top of the incline plane, which means no KE and only PE. That means it starts out with a total E of m*9.8*(2.85*sin 12.2)

At the bottom of the ramp, all that PE has been converted into KE.

KE = 1/2(m)(v^2)

So since E is conserved because there is no friction on the ramp nor air drag, set PE = KE and solve for V. Note that your masses will cancel out.

 

[zcabral]

the mass is not given

 

[Littlepig]

the mass is not given

no problem, if the mass is the same in the begin and in the end, they cut in the equation... state the equation on a paper and you will see

 

[Oerg]

although its much easier to do by consrevation of energy, but you should also reflect on why kinematics did not work for you. Are you still weak in kineatics? You may have escaped from using kinematics from this question but not all questions can be solved by conservation of energy,The correct equation to use would be v^2=u^2+2as. if you used the equation in your OP, then you should have solved quadratically for t and substituted t into (v-u)=at.

 

[physixguru]

this should be enough...

velocity at the bottom of an inclined plane is independent of angle of inclination...

infact it is given by...

v=[(2)gh]^1/2

 

[Oerg]

this should be enough...


v=[(2)gh]^1/2

I think it would be way better to derive this result rather than to mug this equation and plug the numbers into it

 

[physixguru]

I think it would be way better to derive this result rather than to mug this equation and plug the numbers into it

well you are right but is it a too difficult equation my frnd?