A ball is shot horizontally from a spring loaded gun into a pendulum catcher (a

Question

A ball is shot horizontally from a spring loaded gun into a pendulum catcher (a metal contaption to catch the ball, hanging from the end of a 25.0cm string). The mass of the ball is 55.0g and the mass of the catcher is 35.0g. After the collision, the ball and the catcher swing and rise together to a maximum angle of 32.5 degrees.

a) Is energy conserved after to collision?

b) Is energy conserved during the collision?

c) The gun was only compressed 2.35 cm, what was the spring constant of the spring in the gun?

Explanation / Answer

Given

Mass of the ball m = 55 g = 0.055 kg

Mass of the catcher M = 35 g = 0.035 Kg

Length of the string L = 25 cm = 0.250 m

Angle of rise = 32.5o

Compression length x = 2.35 cm = 0.0235 m

Solution

a) Yes , The energy is conserved after collision since there are no external factors that could cause any deformation to the system

b) no, the energy is not conserved during the collision, when the two masses became one a part of their mechanical energy is used in that process, this loss in Kinetic energy will be in the form of heat and sound vibrations

c)

the linear momentums are conserved during collision

let u and v be ball’s velocities before and after collision

hence,

mu = (m+M) v

u = (m+M)v / m

but v = (2gh)

The maximum height h = L - L cos

h = 0.250 – 0.250 cos32.5

h = 0.039 m

v = (2 x 9.8 x 0.039)

v = 0.874 m/s

so u = (0.055 + 0.035) x 0.874 / 0.055

= 1.430 m/s

Initial Kinetic energy of the ball

E = ½ mu2

= 0.05623475 J

This kinetic energy comes from the potential energy of the spring

E = ½ kx2

0.05623475 = ½ k 0.02352

K = 203.66 N/m

Why v = (2gh) ?

When the ball collide with the catcher, they stick together and become one object

The mass of this object = mass of the pendulum (m) + mass of the catcher (M)

It moves with a velocity v upwards until it spend all its kinetic energy is spent in doing work against the gravity. The work done will be stored as it kinetic energy. if the object raises to a height of h meters then

as per conservation of energy

kinetic energy = potential energy

½ (m+M)v2 = (m+M)gh

v2 = 2gh

v = (2gh)

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