Can you help me with No.1 and No.3 What percentage of the kinetic energy is lost

Question

Can you help me with No.1 and No.3

What percentage of the kinetic energy is lost in the collision? Use the masses and velocities to calculate this percentage. % Lost = KE before - KE after/KE before times 100% How does the height to which the pendulum swings change if the ball is bounced off the rubber bumper on the front of the catcher instead of being caught? Try it but be sure to move the catcher farther away from the Launcher so the steel ball won't rebound into the Launcher and damage the Launcher. A bullet of 40 g mass is fired horizontally into a 10 kg block which is suspended as a ballistic pendulum. The impact causes the center of mass of the block to rise 10 cm. Calculate the speed of the bullet just before impact. Believe it or not, this experiment was actually done by your instructor in their equivalent lab. Does the force of gravity affect the horizontal component of the projectile's velocity? Justify answer using physics concepts.

Explanation / Answer

1. mass m1 has velocity v1i and m2 has velocity v2i (before the collision)

after the collision,

m1 -> v1f

m2 -> v2f

%lost = [ m1 v1i^2/2 + m2 v2i^2 /2 - m1v1f^2 /2 - m2 v2f^2 /2 ] / ( m1 v1i^2/2 + m2 v2i^2 /2 ) x 100

= ( m1 v1i^2 + m2 v2i^2 - m1 v1f^2 - m2 v2f^2) (100) / (m1 v1i^2 + m2 v2i^2 )

3. Applying energy conservationt find the speed of block plus bullet after the collision,

m g h = m v^2 / 2

2 x 9.8 x 0.10 = v^2

v = 1.4 m/s

now APPLYING MOmentum conservation to find speed of bullet before the collision,

0.040 x v1i + 0 = (10 + 0.040) x 1.4

v1i = 351.4 m/s ..........Ans

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