Question

While on a playground, you and your niece take turns sliding down a frictionless slide. Your mass is 75 kg while your little niece's mass is only 25 kg. Assume that both of yo begin sliding from rest from the same height. Which one of the following statements b describes who has a larger speed at the bottom of the slide?
a. You, because your greater weight causes a greater downward acceleration.
b. Your niece, because she is not pressing down against the side as strongly her motion is closer to free fall than yours.
c. Both of you have the same speed at the bottom.
d. Your niece, because lighter objects are easier to accelerate.
e. You, because you take less time to slide down.

Answer 1

Answer:

c.

Explanation:

• In absence of friction, total mechanical energy must be conserved.
• This means that the change in gravitational potential energy (in magnitude) must be equal to the change in kinetic energy:

       $\Delta K = \Delta U \\ \\ \frac{1}{2} * m* v^{2} = m*g*h$

• As it can be seen, the mass m is on the both sides of the equation, which means that it can be simplified.
• We can solve this equation for v (speed at the bottom) as follows:

        $v = \sqrt{2*g*h}$

• As it can be seen, the mass has no part in the equation, so, due both are starting from the same height, both people have the same speed at the bottom.
• The option c is the right one.