How to Calculate the Compression Distance of a Spring on an Inclined Plane?

[blade_090]

Homework Statement

an inclined plane of angle 20 degree has a spring of force constant k= 500N/m fastened securely at the bottom so that the spring is parallel to the surface. a block of mass m=2.5kg is placed on the plane at a distance d=0.300m from the spring. From this position, the block is projected downward towards the spring with speed, v=0.750m/s. By what distance is the spring compressed when the block momentarily comes to rest?

Homework Equations

work done of spring=1/2kx2 and kinetic energy=1/2mv2
and potential energy=mglsin20?

The Attempt at a Solution

i try to solve the ques by using work done of spring= potential energy+kinetic energy
bt can't find the correct ans =S
which part i did wrong?

 

[ehild]

Show your work in detail.

ehild

 

[blade_090]

Show your work in detail.

ehild

1/2mv2+mglsin20=1/2kx2
1/2(2.5)(0.75)^2+2.5(9.8)(0.3sin20)=1/2(500)(x)^2
x=0.113m
bt the real ans is o.131m
i wonder which part i did wrong

 

[ehild]

The block travels more than 0.3 m as its compresses the spring by x.

ehild

 

[blade_090]

The block travels more than 0.3 m as its compresses the spring by x.

ehild

ic...so how do i find the distance traveled by the block?
i got to find the acceleration 1st rite?
thru mgsin20=ma?

 

[ehild]

Use the energy equation as before but with the new length the block travels till coming to rest.

ehild

 

[blade_090]

Use the energy equation as before but with the new length the block travels till coming to rest.

ehild

i mean how do find the new length the block travelled?
is the block's acceleration-----mgsin20=ma?

 

[ehild]

Before touching the spring, it is. After touching the spring, it is different. But you do not need the acceleration. Think: what is x? Make a drawing. ehild

 

[blade_090]

Before touching the spring, it is. After touching the spring, it is different. But you do not need the acceleration. Think: what is x? Make a drawing.


ehild

lolx..silly me XDD
i missunderstand ur explanation jus now
i figured it out..
thx for ur help ^^