Question

Two particles of mass 1kg each are moving in opposite direction with speed of 6m/s and 4m/s and undergoes collision with coefficient of restitution= 1/2. Calculate loss in Kinetic energy.

Answer 1

I have solved the question in the pic i have attached below. Hope it helps!

Answer 2

Answer:

The loss of kinetic energy is 18.75J.

Explanation:

Given,

m1 = 1 kg

m2 = 1 kg

u1 = 6 m/s

u2 = 4 m/s

e = 0.5

The velocity after the collision is v1 and v2 of mass m1 and m2 respectively.

So, the velocity of approach,

ua = u1 + u2

and, the velocity of separation is

vs = v2 - v1

The collision has a coefficient of restitution

e = vs/ua

⇒ e = (v2 - v1) / (u1 + u2)

⇒ 0.5 = (v2 - v1) / (6 + 4)

⇒ v2 - v1 = 0.5×10

⇒ v2 - v1 = 5    -(i)

By the law of conservation of momentum,

m1u1 + m2u2 = m1v1 + m2v2

⇒ 1×6 − 1×4 = 1×v1 + 1×v2

​⇒ 6 - 4 = v1 + v2

⇒ v1 + v2 = 2    -(ii)

Solving equations (i) and (ii), we get

v1 = -1.5 m/s

v2 = 3.5 m/s

The initial kinetic energy is,

$K_i = \frac{1}{2}m_1u_1^2 +\frac{1}{2} m_2u_2^2$

Ki = (1/2)×1×6² + (1/2)×1×4²

Ki = (1/2)×(36 + 16)

Ki = (1/2)×52

Ki = 26J

The final kinetic energy is,

$K_f = \frac{1}{2}m_1v_1^2 +\frac{1}{2} m_2v_2^2$

Kf = (1/2)×1×(3.5)² + (1/2)×1×(1.5)²

Kf = (1/2)×(12.25 + 2.25)

Kf = (1/2)×14.5

Kf = 7.25J

The change in kinetic energy is

ΔKE = Kf - Ki

ΔKE = 7.25 - 26

ΔKE = -18.75J

Hence, the loss of kinetic energy is 18.75J.

To learn more about kinetic energy, click on the link below:

https://brainly.in/question/1797886

To learn more about the law of conservation of momentum, click on the link below:

https://brainly.in/question/13464300

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