How high will the pendulum rise?

[tbdm]

Homework Statement

You are given a pendulum composed of a 0.015 kg mass on the end of a 0.40 m long massless string. If the pendulum is moved 30° from the vertical and given an initial speed of 0.45 m/s tangent to the support string and away from the vertical, how much higher relative to the release point of the pendulum swing will the pendulum rise?

Homework Equations

(1/2)mv² + mgh₁ = mgh₂
h=L(1-cosθ)

The Attempt at a Solution

I plugged in the values, using the second equation to find the initial height.
Mass cancels out and I have (1/2)(.45)² + (9.8)(.4)(1-cos(30)) = (9.8)(h₂)

Solving this gives the resultant height of 0.063921 m. Subtract the release height of 0.052518 m, I get that it rises 0.01033≈0.010 meters higher, however this answer is incorrect.

 

[gneill]

Hi tbdm, Welcome to Physics Forums.

Homework Statement

You are given a pendulum composed of a 0.015 kg mass on the end of a 0.40 m long massless string. If the pendulum is moved 30° from the vertical and given an initial speed of 0.45 m/s tangent to the support string and away from the vertical, how much higher relative to the release point of the pendulum swing will the pendulum rise?

Homework Equations

(1/2)mv² + mgh₁ = mgh₂
h=L(1-cosθ)

The Attempt at a Solution

I plugged in the values, using the second equation to find the initial height.
Mass cancels out and I have (1/2)(.45)² + (9.8)(.4)(1-cos(30)) = (9.8)(h₂)

Solving this gives the resultant height of 0.063921 m. Subtract the release height of 0.052518 m, I get that it rises 0.01033≈0.010 meters higher, however this answer is incorrect.

Note that for changes in gravitational PE that take place near the surface of the Earth you are free to set the location of your zero reference height to anything that's convenient. In this problem they're asking for the additional height achieved from the given initial position, so you could just choose the height of that position as the zero reference for gravitational PE as well as height.

To me your solution looks okay. Is there some particular format you're supposed to use to submit it?

 

[tbdm]

I finally tried using all of the significant figures, and that finally seemed to do it, thank you for your help!