Question

A sled of mass m is coasting at a constant velocity on the ice covered surface of a lake. Three birds, with a combined mass 0.5m, gently land at the same time on the sled. The sled and birds continue sliding along the original direction of motion. How does the kinetic energy of the sled and birds compare with the initial kinetic energy of the sled before the birds landed

Answer 1

Complete Question

A sled of mass m is coasting at a constant velocity on the ice covered surface of a lake. Three birds, with a combined mass 0.5m, gently land at the same time on the sled. The sled and birds continue sliding along the original direction of motion. How does the kinetic energy of the sled and birds compare with the initial kinetic energy of the sled before the birds landed?

a) The final kinetic energy is one half of the initial kinetic energy.

b) The final kinetic energy is one third of the initial kinetic energy.

c) The final kinetic energy is one quarter of the initial kinetic energy.

d) The final kinetic energy is one ninth of the initial kinetic energy.

e) The final kinetic energy is equal to the initial kinetic energy

Answer:

The correct option is b

Explanation:

From the question we are told that

   The mass of the sled is  m  

   The  mass of the three birds is  $m_b = 0.5 m$

Generally from the law of momentum conservation,

  The initial momentum of the boat  =  final  momentum of the boat

Hence

     $m * v = (m_b+ m) * v_2$

=>  $m v = (0.5m+ m) * v_2$

=>  $m v = 1.5m* v_2$

Here v is the velocity of the boat before the birds landed and $v_2$ is the velocity after the birds landed

So

       $v_2 = \frac{2}{3} v$

Generally the initial  velocity of the boat before the birds landed is mathematically represented as

      $K_i = \frac{1}{2} * m * v ^2$

Generally the final  velocity of the boat when the birds have landed is mathematically represented as

      $K_f = \frac{1}{2} * (m_b + m ) * v_2^2$

=>   $K_f = \frac{1}{2} * (0.5m + m ) * (\frac{2}{3} v)^2$

=>  $K_f = \frac{1}{2} * 1.5m * (\frac{2}{3} v)^2$

=>  $K_f = \frac{1}{2} * 1.5m * \frac{4}{9} v^2$

=>  $K_f = \frac{1}{2}m v^2 * \frac{1}{3}$

Comparing this equation with that of the initial  kinetic energy

=>  $K_f = \frac{1}{3} K_i$      

Answer 2

The kinetic energy of the sled and birds is one-third the initial kinetic energy of the sled before the birds landed.

What is kinetic energy?

When an object is in motion, then the energy possessed by the object at the state of motion is known as its kinetic energy.

Given data -

The combined mass of three birds is, M = 0.5m.

Let m be the mass of the sled. Then applying the conservation of linear momentum as,

The initial momentum of the boat  =  final  momentum of the boat

mv = (M + m)v'

v is the velocity of the boat before the birds landed and v' is the velocity after the birds landed.

mv = (0.5m + m)v'

mv = 1.5mv'

v = 3/2 v'

or

v' =2/3v

The initial kinetic energy of the boat before the birds landed is mathematically represented as

$K_{1}= \dfrac{1}{2}mv^{2}$

And the final kinetic energy of the boat when the birds have landed is mathematically represented as,

$K_{2}=\dfrac{1}{2}(M+m)v'^{2}\\\\K_{2}=\dfrac{1}{2}(1.5m) \times 4/9v^{2}\\\\K_{2}=\dfrac{1}{3} \times \dfrac{1}{2}mv^{2}\\\\K_{2}=\dfrac{1}{3} \times K_{1}$

Thus, we can conclude that the kinetic energy of the sled and birds is one-third the initial kinetic energy of the sled before the birds landed.

Learn more about kinetic energy here:

https://brainly.com/question/999862