Ballistic pendulum problem Solutionlet m is the mass of stea

Ballistic pendulum problem

let m is the mass of steal marble.

M is the mass of pendulum bob.

v_f is the velocity of bob and marble

v_o is the velocity of marble.

maximum angle given is (theta)=36⁰

(1) engrgy conservation gives ½ (m+M)v_f² = (m+M)gh

So the speed of the system immediately after the collision is: v_f = (2gh)^½ --------------------eq 1

Momentum before: mv_o = momentum after: (m+M)v_f v_o= (2gh)^½(M + m)/m.-----------------eq 2

maximum height= v_f² /2g

in terms of theta h max = L(1-cos 36⁰ )=0.715(1-0.85)=0.1073m

(2) gravitational potential energy is (m+M)gh= (0.010+0.5782)x9.8x0.1073=0.62joule

(3) since we know the value og h , so from equation 1we can calculate v_f = 1.5m/sec

hence the kinetic energy of the masses at the bottom of the swing= 1/2(m+M)v_f² = 1/2(0.5882)x 1.5x1.5=0.6617 joule

(4) from eq 1 the speed of the masses = 1.5 m/sec

(5) now we know v_f , so from eq 2 we have v= v_f (m+M)/m= 1.5(0.5882)/0.010 =88.23m/sec