Physics
13.07.2020 02:32
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A 4.0 kg circular disk slides in the x- direction on a frictionless horizontal surface

A 4.0 kg circular disk slides in the x- direction on a frictionless horizontal surface with a speed of 5.0 m/s as shown in the adjacent Figure. It collides with an identical disk that is at rest before the collision. The collision is elastic. Disk 1 goes off at an 60 5.0 m/s angle of 60 with respect to the x-direction. Disk 2 g 30 goes off at an angle of 30 with respect to the x-direction. What best describes the speeds of the disks after the collision?
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officialkk
officialkk
4,7(80 marks)

Solution :

Let $m_1=m_2=4$ kg

$u_1 = 5$ m/s

Let $v_1$ and $v_2$ are the speeds of the disk $m_1$ and $m_2$  after the collision.

So applying conservation of momentum in the y-direction,

$0=m_1 .v_1_y -m_2 .v_2_y $

$v_1_y = v_2_y$

$v_1 . \sin 60=v_2. \sin 30$

$v_2 = v_1 \times \frac{\sin 60}{\sin 30}$

$v_2=1.732 \times v_1$

Therefore, the disk 2 have greater velocity and hence more kinetic energy after the collision.

Now applying conservation of momentum in the x-direction,

$m_1.u_1=m_1.v_1_x+m_2.v_2_x$

$u_1=v_1_x+v_2_x$

$5=v_1. \cos 60 + v_2 . \cos 30$

$5=v_1. \cos 60 + 1.732 \times v_1 \cos 30$

$v_1 = 2.50$ m/s

So, $v_2 = 1.732 \times 2.5$

          = 4.33 m/s

Therefore, speed of the disk 2 after collision is 4.33 m/s

Caleb0018
Caleb0018
4,8(92 marks)

Work done by the crane is 150,000 J

Explanation:

Work done by an object is defined as the amount of energy being transferred from one object to another over a distance by applying force on it.The formula to find work done is work done, W = F d, where F is the force applied and d is the distance at which you applied the force.

Given parameters are,

Force applied, F = 1000 N

Distance, d = 150 m

Hence, apply in the formula, W = 1000 X 150 = 150,000 J

Work done by the crane is 150,000 J

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