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

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In summary, the conversation is about finding the distance the spring is compressed when a block is projected towards it on an inclined plane. The person initially used the equation for work done by the spring, but was unable to find the correct answer. Upon further discussion, it was determined that the block travels more than the initial distance of 0.3m as it compresses the spring, and the person was advised to use the energy equation to find the new distance traveled. After some clarification, the person understood and was able to solve the problem.
  • #1
blade_090
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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?
 
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  • #2
Show your work in detail.

ehild
 
  • #3
ehild said:
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
 
  • #4
The block travels more than 0.3 m as its compresses the spring by x.

ehild
 
  • #5
ehild said:
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?
 
  • #6
Use the energy equation as before but with the new length the block travels till coming to rest.

ehild
 
  • #7
ehild said:
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?
 
  • #8
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
 
  • #9
ehild said:
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 ^^
 

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