A 24g rifle bullet traveling 270 m/s buries itself in a 3.8kg pendulum hanging on a 2.8m long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum's displacement.
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the velocity of the pendulum is
v = m1*v1/(m1+m2) where m1 = mass of bullet, m2 = mass of bob, v1 = velocity of bullet
v = 0.024*270/3.824 = 1.694 m/s
the kinetic energy of the combined bob + bullet is
Ekin = 1/2*3.824*1.694^2 = 5.49 J
this energy is converted into potential energy:
5.49 = mgh
h = 5.49/(mg) = 5.49/(3.824*9.81)
h = 0.146 m (this is the y coordinate)
the x coordinate is found by Pythagoras:
x^2 = 2.8^2 - (2.8 - 0.146)^2
x = 0.8934 m (this is the x coordinate)
displacement = (0.8934, 0.146)
O.G.
v = m1*v1/(m1+m2) where m1 = mass of bullet, m2 = mass of bob, v1 = velocity of bullet
v = 0.024*270/3.824 = 1.694 m/s
the kinetic energy of the combined bob + bullet is
Ekin = 1/2*3.824*1.694^2 = 5.49 J
this energy is converted into potential energy:
5.49 = mgh
h = 5.49/(mg) = 5.49/(3.824*9.81)
h = 0.146 m (this is the y coordinate)
the x coordinate is found by Pythagoras:
x^2 = 2.8^2 - (2.8 - 0.146)^2
x = 0.8934 m (this is the x coordinate)
displacement = (0.8934, 0.146)
O.G.