Question

A 1-lb block and a 100-lb block are placed side by side at the top of a frictionless hill. Each is given a very light tap to begin their race to the bottom of the hill. In the absence of air resistance, what can you conclude about the outcome of the race?

a)The 1-lb block wins the race.b)The 100-lb block wins the race.c)The two blocks end in a tie.d)There’s not enough information to determine which block wins the race

Answer 1

The answer is c)The two blocks end in a tie

Explanation (See attachment):

Let´s solve the general problem:

The hill is an inclined plane. We know there is no friction and no air resistance.

Let´s solve by using Energy equations and energy conservation law. At the top of the hill when the block is not moving it has a Potential Energy, as soon as it starts moving, all that Potential Energy starts converting to Kinetic Energy until it reaches the end of the hill:

1) At the top of the inclined plane we have a block of mass "m" with potential energy of
`Ep = mgh`, where "m" is mass, "g" is gravity acceleration and "h" is height.

2) Just an instant before the block hits the bottom, it has a Kinetic Energy of
`Ek = (1)/(2) mv^(2)` where "m" is mass, and "v" is velocity

Thanks to energy conservation law we know that Ep = Ek:

• 
  `mgh = (1)/(2) mv^(2)`
• 
  `v = √(2gh)`

As we can see in our last equation, mass cancels out. This means that mass does not play a role in how fast this object slides down the inclined plane.

In conclusion, it doesn´t matter how much mass or how heavy the block is, it is going to slide down at the exact same velocity in a frictionless slide and without air resistance. This means, a 1lb block and a 100lb block will reach the bottom of the hill at the same time.