u = (30 kg) (30 m/s) + (20 kg) (20 m/s) / ((30 kg) + (20 kg))
= 26 (m/s)
A rifle weighing 6 lb fires a bullet weighing 0.035 lb with muzzle speed 2100 ft/s. The total momentum of the rifle and bullet can be expressed as
ML = mr vr + mb vb
= mr ur + mb ub
The rifle and the bullet are initially at rest (vr = vb = 0):
ML = (6 lb) (0 ft/s) + (0.035 lb) (0 ft/s)
= (6 lb) ur (ft/s) + (0.035 lb) (2100 ft/s)
The rifle recoil speed:
ur = - (0.035 lb) (2100 ft/s) / (6 lb)
= - 12.25 (ft/s)
The recoil kinetic energy in the rifle can be calculated as
E = 1/2 m ur2
= 1/2 (6 lb) (-12.25)2
= 450 lb ft
The force required to slow down a recoil depends on the slow down distance. With a slow down distance s = 1.5 in (0.125 ft) - the acting force can be calculated as
F = E / s
= (450 lb ft) / (0.125 ft)
= 3600 lb
Angular momentum for a rotating body can be expressed as
MR = ω I (3)
MR = angular momentum of rotating body (kg m2 / s, lbf ft s)
ω = angular velocity (rad/s)
I = moment of inertia - an object's resistance to changes in rotation direction (kg m2, slug ft2)
The conservation of angular momentum can be expressed as
ω1 I1 = ω2 I2 (4a)
n1 I1 = n2 I2 (4b)
n = rotation velocity in revolutions per minute (rpm)
For a small point mass I = m r2 and ω = v / r and 4a can be modified to
m v1 r1 = m v2 r2 (4c)
v1 r1 = v2 r2 (4d)
ω1 r1 = ω2 r2 (4e)
n1 r1 = n2 r2 (4f)
v = tangential velocity (m/s, ft/s)
r = radius (m, ft)
A small iron sphere rotates around an axis with velocity 100 rpm when connected to a rope with length 1.5 m. The rope is extended to 2.5 m and due to conservation of angular momentum the new velocity can be calculated by modifying 4f to
n2 = n1 r1 / r2
= (100 rpm) (1.5 m) / (2.5 m)
= 60 rpm
Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.
Change in velocity vs. time used.
Angular velocity and acceleration vs. power and torque.
Forces due to circular motion and centripetal / centrifugal acceleration.
Linear and angular (rotation) acceleration, velocity, speed and distance.
Impact forces acting on falling objects hitting the ground, cars crashing and similar cases.
Forces acting a very short time are called impulse forces.
Energy possessed by an object's motion is kinetic energy.
Calculate the range of a projectile - a motion in two dimensions.
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