How do I work the 2nd part of this problem?

Question

A projectile of mass 0.900 kg is shot straight up with an initial speed of 22.0 m/s.

(a) How high would it go if there were no air friction?

I got this right with 24.7 meters

(b) If the projectile rises to a maximum height of only 16.5 m, determine the magnitude of the average force due to air resistance.

I'm not exactly sure how to calculate the air resistance. Can someone help?

Thanks James!

Answer 1

Okay, if the projectile should have gone 24.7 meters up but only went 16.5 meters, the friction took away .9*9.8*(24.7-16.5) =72.32 jouls of energy; since friction did this over 16.5 meters, the average force of friction was 72.32/16.5=4.38 newtons.

Answer 2

Find the potential energy difference between the two heights. The difference is what is lost to air resistance, which acts over a distance of 16.5 m. Since energy = F * D, the average force is the energy loss / distance.

Answer 3

Then air resistance is causing deceleration.
use the formula f = ma
first you have to get the acceleration so use the formula of motion
v^2 = u^2 + 2as
0 = 22^2 + 2(a)(16.5) get the acceleration from this formula and then plug it into the f =ma formula with the mass of the projectile and you got your force ;-)

Answer 4

Ok, first you draw your free body diagram, with that you can see that the force acting on the proyectile is friction + mg where m is mass and g is the gravity acceleration.

then you get that the acceleration is going to be friction acceleration + g

y = (Vf2-Vo2)/(2*(a+g))

since Vf =0 you get

y = -Vo2/(2*(a+g))

since you are assuming that the positive direction is upwards, then the acceleration is going to be negative, so

y = Vo2/(2*(a+g))

you solve for a and you get

a= Vo2/(2*y)-g

a= (22m/s)squared/(2*16.5m)-9.81m/s2

a= 4.86 m/s2

Now to get the force caused by the air friction you just multiply the acceleration per the mass because

F = ma

F = 0.9 kg * 4.86 m/s2

F = 4.37 N

hope this helps.

Answer 5

first of all calculate work done by weight for a displacement of 24.7m.then calculate work done by force for displacement of 16.5m.then difference of these work done gives work done by air resistance.now divide this work by 24.7m-16.5m,then get your answer.