Falling Stuff. Do Falling Objects Accelerate?. It sure seems like it! Starts from rest, goes faster and faster.... What about a feather, though? Air resistance, drag Terminal velocity What if we could get rid of the air? What’s responsible for the downwards force?
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F = ma
“g”= 9.8m/s2 = 32 ft/s2
Since F = ma, the gravitational force must be proportional to mass.
Consider two identical falling objects
Now imagine two more, connected together with a tiny thread
Mass of each = M Total Mass = 2 M
But they all have the same acceleration!
Force on the joined balls must be twice the force on one of them, since the mass doubled but the acceleration stayed the same.
Conclusion: Gravitational force must be proportional to mass
Experimental tests show the Universality of Free Fall is the same for different materials to within 0.00000000001%
If the gravitationally induced acceleration is the same for all objects at the surface of the Earth, then
Force exerted by gravity = (mass) (acceleration due to gravity)
Fgravity = m g = WEIGHT, where g = 9.8 m/s2
For a mass of 100 kg, force from gravity at Earth’s surface is
F = 100 kg 9.8 m/s2 = 980 Newtons.
(An apple weighs about 2 N, a golf ball weighs 1.4 N)
After an interval t, the velocity changes by an amount at, so that
vfinal = vinitial + at
How fast was it going at the end of 3 sec?
vinitialwas 20 m/s after 2 sec
a was 10 m/s (as always)
t was 1 sec (interval)
vfinal = 20 m/s + 10 m/s2 1 s = 30 m/s
The average velocity in the interval is just
Vavg = ½(vinitial + vfinal)
For the 1 – 2 s interval,
vi = 10 m/s vf = 20 m/s
So vavg = ½ (10+20) m/s
= 15 m/s
Starting from rest, letting go:
vfinal = v(t) = vinit + at
x(t) = xinit + vavgt
x(t) = xinit + vinitt + ½at2