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In a ballistic pendulum experiment, a small marble is fired into a cup attached to the end of a pendulum. If the mass of the marble is 0.0265 kg and the mass of the pendulum is 0.250 kg, how high will the pendulum swing if the marble has an initial speed of 5.05 m/s? Assume that the mass of the pendulum is concentrated at its end so that linear momentum is conserved during this collision.

Respuesta :

Answer:

0.012 m

Explanation:

m = mass of the marble = 0.0265 kg

M = mass of the pendulum = 0.250 kg

v = initial velocity of the marble before collision = 5.05 m/s

V = final velocity of marble-pendulum combination after the collision = ?

using conservation of momentum

m v = (m + M) V

(0.0265) (5.05) = (0.0265 + 0.250) V

V = 0.484 m/s

h = height gained by the marble-pendulum combination

Using conservation of energy

Potential energy gained by the combination = Kinetic energy of the combination just after collision

(m + M) gh = (0.5) (m + M) V²

gh = (0.5) V²

(9.8) h = (0.5) (0.484)²

h = 0.012 m

fichoh

Using the concept of inelastic collison and principle of conservation of momentum, the height of swing made by the pendulum would be 0.012 meters

Collison is inelastic :

  • m1v1 = (m1 + m2)v
  • v = final velocity after the collision

(0.0265 × 5.05) = (0.0265 + 0.250)v

0.133825 = 0.2765v

v = (0.133825 ÷ 0.2765)

v = 0.484 m/s

Final velocity after collision = 0.484 m/s

Assuming linear momentum is conserved :

  • Kinetic energy = Potential Energy

0.5mv² = mgh

Mass cancels out

0.5v² = gh

0.5(0.484)² = 9.8h

9.8h = 0.1171

h = (0.1171) ÷ 9.8

h = 0.0119

Therefore, height of the swing made by the pendulum would be 0.012 meters.

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