Question

Two blocks of ice, one four times as heavy as the other, are at rest on a frozen lake. A person pushes each block the same distance d. Ignore friction and assume that an equal force is exerted on each block. Which of the following statements is true about the kinetic energy of the heavier block after the push?

Answer 1

Answer:

The kinetic energy of the heavier block after the push is equal to the kinetic energy of the lighter block

Explanation:

Kinetic energy of smaller object

$K=(1/2)mv^2$

where m= mass of smaller object and v= velocity of smaller object

Also, it is given that heavier object is four times the mass of lighter object and consider its velocity as V

kinetic energy of heavier block $K '= (1/2) (4m) V^2$

Now, For smaller block , $v^2 - u^2=2aS$

[by Newtons laws of motion]

Also, $v^2 = 2(F/m)S$

Where S= displacement, F= force, u= initial velocity

So, $K=(1/2)m[2(F/m)]S$

$\Rightarrow K = FS$

For heavier block ,

$V^2 - u^2 = 2a'S$

or,  $V^2=2(F /4m)S$

So,$K '= (1/2)(4m)[2(F/4m)S$

$\Rightarrow K'= FS$

Therefore the kinetic energy of the heavier block after the push is equal to the kinetic energy of the lighter block