Launching a Potato with a Spring: Solving for the Spring Constant

[OnceKnown]

Homework Statement

A Certain potato "canon" consists of a 1.2 m tube with a thin platform inside. The Platform has a negligible mass and is attached to a spring. The spring is 20 cm long when relaxed, and the spring is compressed to a final length of 5 cm when ready to launch a potato. A potato is placed in the tube, touching the platform. This particular potato has a mass of 375 g and a length of 10cm. There is an average frictional force of 2.8 N between the potato and the inside of the tube. When the spring is released the potato is launched.

1) What is the value of the spring constant such that the potato has a range of 30 cm when fired in the orientation of 40 degrees with respect to the horizontal plane.

Homework Equations

Force of spring = (k)(Δx)

The Attempt at a Solution

I thought about using the formula R = (v^2(initial) * sin2θ)/g
where R is the range. But I'm not exactly sure if using that formula would be correct.

Would that v(initial) be the velocity that leaves the launcher and from there we need to find out what spring constant would give that amount of launch velocity?

I don't know where to begin. Please help.

Does the potato have to end on the same height to use the above formula?

 

[LawrenceC]

"Does the potato have to end on the same height to use the above formula?"

Yes, it does.

Hint:

Determine the time of flight needed for the spud to travel 0.30 m in terms of unknown horizontal velocity, Vh, as the spud leaves the tube.

Use this unknown time in terms of Vh as a 'plug in' for the time in the vertical displacement equation. You know the ratio of Vv/Vh due to elevation of tube. This equation will provide you with a hard number for Vh at the moment the spud leaves the tube.

Then use work-energy relations to achieve the velocity as the spud leaves the tube.

 

[OnceKnown]

Okay. Can you go over on how flight time is calculated for this problem? I've been stuck on that part the most.

 

[The Anonymous]

Well, you could come to office hours and ask me yourself, or you could do the following...

Rearrange the horizontal equation for range to solve for time. Insert that 't' into the vertical displacement equation and isolate the initial speed. That'll tell you how fast the potato needs to be moving when it leaves the launcher in order to travel the 30 meters.

cheersPS - the relevant equation is already solved for you and presented in chapter 4.

cheersPPS - the range should be 30 meters, not cm...read carefully.

cheers

 

[OnceKnown]

Hi Professor!

Sorry that I couldn't come to you in person about the problem. Having work on the days where you were free for office hours really clashes in time.

Thank you so much for the help though.

(Pretty shocking to find you on here):shy:

 

[The Anonymous]

Email me if you have more questions,


cheers