A projectile of mass 0.800 kg is shot straight up with an initial speed of 28.0 m/s.
(a) How high would it go if there were no air friction?
(b) If the projectile rises to a maximum height of only 26.8 m, determine the magnitude of the average force due to air resistance.
I got the correct answer for part A, it's part B that's giving me trouble. I tried using 1/2 mv2=Fd but it seems that I'm missing something.
Good work on part (a). I will assume you got 40 meters for the answer
For part (b), there is a potential energy deficit of (40 - 26.8)*M*g at the top of the trajectory. Set this equal to work done against friction, F*26.8 m, and solve for F.
With your equation, you were assuming that ALL of the initial kinetic energy went into friction work. Only some of it did.
Ahh, gotcha. Thanks a lot for clearing that up.
To find the magnitude of the average force due to air resistance, you can use the work-energy principle. The work done by the force of air resistance is equal to the change in kinetic energy of the projectile.
In this case, since the projectile rises to a maximum height and comes to rest, the work done by the force of air resistance is equal to the initial kinetic energy of the projectile.
The initial kinetic energy of the projectile can be calculated using the formula:
KE = 1/2 * m * v^2
where KE is the kinetic energy, m is the mass of the projectile, and v is the initial velocity.
Substituting the given values:
KE = 1/2 * 0.800 kg * (28.0 m/s)^2
Simplifying the above equation, we can find the value of the initial kinetic energy.
Once we have the value of the initial kinetic energy, we can conclude that the work done by the force of air resistance is equal to this value.
Therefore, the magnitude of the average force due to air resistance is equal to the work done by this force, which is equal to the initial kinetic energy of the projectile.