The ball's maximum speed relative to the vehicle?

[Vanessa Avila]

Homework Statement

Inside a NASA test vehicle, a 3.50-kg ball is pulled along by a horizontal ideal spring fixed to a friction-free table. The force constant of the spring is 226 N/m . The vehicle has a steady acceleration of 5.00 m/s2, and the ball is not oscillating. Suddenly, when the vehicle's speed has reached 45.0 m/s, its engines turn off, thus eliminating its acceleration but not its velocity.

What will be the ball's maximum speed relative to the vehicle?

Homework Equations

v = ±ω√(A² - x²)
ω = √(k/m)

The Attempt at a Solution

[/B]
I solved for ω and got 8.0356 rad/s
I tried to use the v equation above and set x = 0 and got 0.598m/s, the site told me my answer was not quite right possibly due to a round-off error.

 

[TSny]

I solved for ω and got 8.0356 rad/s

OK, that looks good.

I tried to use the v equation above and set x = 0 and got 0.598m/s, the site told me my answer was not quite right possibly due to a round-off error.

What value did you use for A and how did you get it?

 

[Vanessa Avila]

OK, that looks good.

What value did you use for A and how did you get it?

I used 0.0774 m for A. I go that by kx=m(a), solved for x and had that equal to A.

 

[TSny]

I used 0.0774 m for A. I go that by kx=m(a), solved for x and had that equal to A.

OK, good. When I use your values of A and ω, I don't get your answer of 0.598 m/s. Maybe you plugged in 0.0744 instead of 0.0774?

 

[Vanessa Avila]

OK, good. When I use your values of A and ω, I don't get your answer of 0.598 m/s. Maybe you plugged in 0.0744 instead of 0.0774?

I did plug in 0.0744! Thank you! I'm being very clumsy today and making really clumsy mistakes. I looked at what i wrote just now and saw that from 0.0774 i changed it to 0.0744. Many thanks! This kinda confused me though. How do we know when to set the x to 0?

 

[Vanessa Avila]

OK, good. When I use your values of A and ω, I don't get your answer of 0.598 m/s. Maybe you plugged in 0.0744 instead of 0.0774?

Did you get 0.622m/s?

 

[TSny]

How do we know when to set the x to 0?

In this problem, you want maximum speed. So, you pick the value of x that will give max speed.

 

[TSny]

Did you get 0.622m/s?

Yes.

 

[Vanessa Avila]

In this problem, you want maximum speed. So, you pick the value of x that will give max speed.

when x is equal to 0, does that always indicate maximum speed at that displacement?

 

[TSny]

For a mass moving only under the influence of a spring, you will get maximum KE (therefore, max speed) when the PE is minimum. Minimum PE for a spring occurs at what value of x?

 

[Vanessa Avila]

For a mass moving only under the influence of a spring, you will get maximum KE (therefore, max speed) when the PE is minimum. Minimum PE for a spring occurs at what value of x?

at its equilibrium point? x=0?

 

[TSny]

at its equilibrium point? x=0?

Right. At the equilibrium point, the spring is unstretched and there is no potential energy stored in the spring. So, all of the energy of the system must be in the form of kinetic energy.

 

[Vanessa Avila]

Right. At the equilibrium point, the spring is unstretched and there is no potential energy stored in the spring. So, all of the energy of the system must be in the form of kinetic energy.

That makes more sense now. Thank you!