Question

# Consider object-1 of mass m1=652gram moving on the +X axis with the velocity of v1=13.5 m/s....

Consider object-1 of mass m1=652gram moving on the +X axis with the velocity of v1=13.5 m/s. Object-1 collide with stationary object-2 of mass m2=846gram on the X-axis. After collision, both objects are moving X-axis. a) Consider the collision is inelastic, and two objects combined into one object after the collision. Find the velocity of the combined object after collision? Consider the collision remains about 1.82ms. find the impulse acts on object-1 during the collision . Find the energy lost due to collision?

here,

the mass of object 1 , m1 = 652 g = 0.652 kg

initial velocity of 1 , u1 = 13.5 m/s

the mass of object 2, m2 = 846 g = 0.846 kg

a)

let the final velocity of combined object be v

using conservation of momentum

m1 * u1 = (m1 + m2) * v

0.652 * 13.5 = (0.652 + 0.846) * v

solving for v

v = 5.88 m/s

the final velocity of combined object is 5.88 m/s

b)

the impulse acts on object 1 , I = m1 * ( v - u1)

I = 0.652 * ( 5.88 - 13.5) kg.m/s

I = - 4.97 kg.m/s

c)

the energy lost in the collison , U = KEi - KEf

U = 0.5 * m1 * u1^2 - 0.5 * (m1 + m2) * v^2

U = 0.5 * ( 0.652 * 13.5^2 - (0.652 + 0.846) * 5.88^2) J

U = 33.5 J