A 2.0 g particle moving at 8.2 m/s makes a perfectly elastic head-on collision w
ID: 1703788 • Letter: A
Question
A 2.0 g particle moving at 8.2 m/s makes a perfectly elastic head-on collision with a resting 1.0 g object.(a) Find the speed of each after the collision. 2.0 g particle 1 m/s
1.0 g particle 2 m/s
(b) Find the speed of each particle after the collision if the stationary particle has a mass of 10 g. 2.0 g particle 3 m/s
1.0 g particle 4 m/s
(c) Find the final kinetic energy of the incident 2.0 g particle in the situations described in (a) and (b). KE in part (a) 5 J
KE in part (b) 6 J
In which case does the incident particle lose more kinetic energy?
7
case (a)
case (b)
.
Explanation / Answer
Given
m1 = 2 g
u1 = 8.2 m/s
m2 = 1 g
u2 = 0
here the collision is elastic collision the momentum and energy of the system is conserved .
let v1 and v2 be the velocities of the particles after collision respectively
m1u1 + m2 u2 = m1 v1 + m2v2
m1 u1 = m1v1 + m2 v2
m1 ( u1 - v1 )= m2 v2 .........(1)
1/2 m1 u1 ^2 + 1/2 m2 u2 ^2 = 1/2 m1v1^2 + 1/2 m2 v2 ^2
m1 u1 ^2 = m1 v1^2 + m2v2^2
m1 *( u1^2 - v1 ^2 ) = m2 v2 ^2 ...........(2)
dividing equation (2) by (1)
u1 + v1 = v2 .........(3)
sub stitute equation (3) in equation (1)
m1 ( u1 - v1 )= m2 (u1 + v1 )
(m1 - m2 ) u1 = (m1 + m2 )v1
after collision
velocity of particle 1 is
v1 = (m1 - m2 / m1+m2 ) u1
= (2-1 / 2+1 ) 8.2
= 2.733 m/s
velocity of particle 2 is
v2 = u1 + v1
= 2.733 + 8.2
= 10.933 m/s
b) if m 2 = 10 g
u1 = 3 m/s
m1 = 2 g
after collision
velocity of particle 1 is
v1 = - 8 / 10 * 3
= -2.4 m/s
v2 = 3 + ( -2.4 ) = 0.6 m/s
c) final kinetic energy of incident particle in part a is
1/ 2 m v^2
1/ 2 ( 2 ) (2.733)^2 = 7.46 J
in part b is
1/2 m ( -2.4 )^2 = 5.76 J
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