Question

a ball, starting from rest, requires a speed of 10 m/s when a force is applied for a distance of 40 m. if the ball has a mass of 5 kg, what is the force being applied?

Answer 1

Okay, you can tell this is an energy problem, as opposed to an acceleration problem, because they give you force and distance as opposed to force and time.

Answer 2

So you want to first find the kinetic energy of the ball.\[\Large E_{kinetic}=\frac{1}{2}mv^2\]

Answer 3

Now work is just the change in energy. Since the ball started at rest, it started at 0 energy so\[\Large E_{work} = E_{kinetic} - 0 = E_{kinetic}\]

Answer 4

Work is force times distance so:
\[\Large E_{work}=Fd\]\[\Large F = \frac{1}{d}E_{work}\]

Answer 5

Combine it all together and we get:\[F=\frac{1}{d}\frac{1}{2}mv^2\]Where \(d = 20m\), \(m=5kg\), and \(v=10m/s\)

Answer 6

@raytiller1 I couldn't have made it any easier for you without giving you the answer.

Answer 7

so \[\frac{ 1 }{ 20 }\frac{ 1 }{ 2 } 20(10)\]

Answer 8

@wio

Answer 9

You need to square velocity

Answer 10

You also need to look at my formula and understand what I did.