Accelerating Proton: Calculating Speed and Kinetic Energy

[wadesweatt]

Homework Statement

A proton (mass m = 1.67x10^-27 kg) is being accelerated along a straight line at 2.0x10^15 m/s^2 in a machine. The proton has an initial speed of 2.4x10^7 m/s and travels 2.5 cm.

(a) What is its speed?

(b) What is the increase in its kinetic energy?

The Attempt at a Solution

Is it ok to have no idea where to begin?

I know F=ma, and that V=Vo+1/2at... but I can't see how that helps.

Help me begin?

 

[LowlyPion]

1. Homework Statement

A proton (mass m = 1.67x10^-27 kg) is being accelerated along a straight line at 2.0x10^15 m/s^2 in a machine. The proton has an initial speed of 2.4x10^7 m/s and travels 2.5 cm.

(a) What is its speed?

(b) What is the increase in its kinetic energy?

3. The Attempt at a Solution

Is it ok to have no idea where to begin?

I know F=ma, and that V=Vo+1/2at^2... but I can't see how that helps.

Help me begin?

You just need two equations.

Kinetic energy.

And an equation that relates Velocity, distance and acceleration.
https://www.physicsforums.com/showpost.php?p=905663&postcount=2

 

[ffrog]

no lowly pion you are wrong what he needs is the other SUVAT equations namely.

S=0.5(u+v)t then rearrange to get V
(u is intitial velocity)

then you put that into the the kenetic energy equation

KE=0.5mv^2

then you have got your anser

 

[LowlyPion]

no lowly pion you are wrong what he needs is the other SUVAT equations namely.

S=0.5(u+v)t then rearrange to get V
(u is intitial velocity)

then you put that into the the kenetic energy equation

KE=0.5mv^2

then you have got your anser

And what is the time the proton is in the machine?

 

[wadesweatt]

You just need two equations.

Kinetic energy.

And an equation that relates Velocity, distance and acceleration.
https://www.physicsforums.com/showpost.php?p=905663&postcount=2

So, using v^2 = v_0^2 + 2a(Delta x), I can find the final velocity I think. For the delta x part, would it be (2.5 - 0)?

And can I use KE= 1/2mv^2 to find the kinetic energy? If so, wouldn't I use the final velocity found in part a for "v"?

Thanks.

 

[LowlyPion]

So, using v^2 = v_0^2 + 2a(Delta x), I can find the final velocity I think. For the delta x part, would it be (2.5 - 0)?

And can I use KE= 1/2mv^2 to find the kinetic energy? If so, wouldn't I use the final velocity found in part a for "v"?

Thanks.

Yes the V² = Vi² + 2ax should do you well.

Part b) is looking for ΔKE. So you are needing to calculate the final KE and subtract the initial.

 

[wadesweatt]

Yes the V² = Vi² + 2ax should do you well.

Part b) is looking for ΔKE. So you are needing to calculate the final KE and subtract the initial.

Ahhhh so I do change in KE=m(v_f)^2 - m(v_i)^2 , right?

 

[LowlyPion]

Ahhhh so I do change in KE=m(v_f)^2 - m(v_i)^2 , right?

Half right anyway.

... i.e don't forget the 1/2.

 

[wadesweatt]

Half right anyway.

... i.e don't forget the 1/2.

haha yes! I knew that I was just typing in a hurry.

Thanks.