using the work-kinetic energy theorem:
.5mvo^2 + Fo/c = .5 mv1^2 where v1 is the velocity at x max I got the following but it is not formatted proprerly. Where am I wrong?
.5vo^2 +Fo/c*m = .5v1^2
vo^2 + 2Fo/c*m = v1^2
sqrt (vo^2 + 2Fo/c*m) = v1
What is c?
m to the -1 power
c= m to the -1 power
then I don't understand your second term:
Fo/c*m if c= m^-1, then
Fo/(1/m *m)=Fo
which is not right. YOu cant add Fo to KE to have work energy.
You have correctly applied the work-kinetic energy theorem equation, but there seems to be a mistake in your simplification. Let's go through the steps again to identify where the error occurred.
The work-kinetic energy theorem states that the work done on an object is equal to the change in its kinetic energy. It can be expressed as:
W = ΔKE
where W is the work done, ΔKE is the change in kinetic energy, m is the mass of the object, vo is the initial velocity, v1 is the final velocity, and Fo/c represents an external force acting on the object over a distance x.
To solve for v1, we can start with the equation:
0.5mvo^2 + Fo/c = 0.5mv1^2
First, let's multiply both sides of the equation by 2 to eliminate the 0.5 factor:
mvo^2 + 2(Fo/c) = mv1^2
Now, let's isolate v1 by subtracting mvo^2 from both sides of the equation:
2(Fo/c) = mv1^2 - mvo^2
Next, let's divide both sides of the equation by m to isolate v1^2:
2(Fo/c)m = v1^2 - vo^2
Finally, to solve for v1, we take the square root of both sides of the equation:
√(2(Fo/c)m) = √(v1^2 - vo^2)
So the correct equation for v1 is:
v1 = √(vo^2 + 2(Fo/c)m)
Therefore, your original equation should be:
v1 = √(vo^2 + 2(Fo/c)m)
Make sure to double-check your calculations and ensure that you're using the proper values for all variables involved.