Block sliding down incline and compressing spring on 30° plane

[teme92]

Homework Statement

Using the Principle of Conservation of Energy, solve:

A block of mass 5kg is released from rest and slides down a distance D
down a smooth plane inclined at 30◦ to the horizontal. It then strikes a
spring compressing it 10cm before it begins to move up the plane. If the
spring constant is 980N/m and g = 9.8m/s2, find D.

Homework Equations

mgh=0.5(k)(x^2)

d=hcos(theta)

The Attempt at a Solution

Using mgh=0.5(k)(x^2)

5(9.8)h=0.5(980)(.01)^2

and got h on its own for:

h=0.001

Then I used d=hcos(theta) to get:

d= (.001)cos(30)

d= 8.66×10^-4

Is this the correct way of doing the question? Thanks for any advice.

 

[cepheid]

Your trig is wrong. D is the hypotenuse of the triangle, and h is the side opposite the angle. Draw a picture.

 

[teme92]

Hi cepheid thanks for the quick reply.

I see so d=h/sin30 then is it?

 

[cepheid]

Hi cepheid thanks for the quick reply.

I see so d=h/sin30 then is it?

That is correct. The rest of your work (applying the conservation of energy( looks fine.

 

[teme92]

Brilliant! Thanks a million for the help!