Calculating Initial Speed of 2.7g Ball Launched at 45° with 50V Solenoid Input

[Hooke's Law]

Homework Statement

A ball ( 2.7 g ) is launched at a 45 degree angle with a solenoid input of 50V. What is the initial speed of the ball?

Homework Equations

KE = 0.5mv^2
PE = mgh
dy = vy(0)t + 0.5at^2
dx = vx(0)t

The Attempt at a Solution

Voltage is potential energy and I think the mechanical energy is being conserved so:

PE=KE

50 J = 0.5mv^2
sqrt(50 J*2/0.0027 kg) = v
192.5 m/s = v

I believe this speed is wrong, because it is numerically huge. Can someone tell me how to do it?

Thanks

 

[thebigstar25]

I have a question for you, why did you say that 50 volt is 50 jole?

 

[I like Serena]

Hi Hooke's Law!

You are referring to a solenoid input of 50 V.

Can I assume that you meant 50 J instead of 50 V, that is, joules instead of volts?

In that case your calculation is correct.
It can be a pretty high speed due to the mass that is pretty low.

Cheers!

 

[thebigstar25]

Hi Hooke's Law!

You are referring to a solenoid input of 50 V.

Can I assume that you meant 50 J instead of 50 V, that is, joules instead of volts?

In that case your calculation is correct.
It can be a pretty high speed due to the mass that is pretty low.

Cheers!

I don't get it! .. how can we make such statement?

 

[I like Serena]

I don't get it! .. how can we make such statement?

If you put 50 joules of energy into a solenoid, that will be converted into kinetic energy.
This is conservation of energy, where we're neglecting any energy that is converted into waste heat.

To do this you would need to set a voltage on the solenoid, generating a current for a certain time. The product of these (or rather the integral) yields the total energy invested in the solenoid.