Question

Two masses sit at the top of two frictionless inclined planes that have different angles. Which mass gets to the bottom first?

Answer 1

Answer:

Explanation:

Let the two inclined planes having angle of inclinations α and β.

The acceleration along the inclined plane acting on the body is gSinα and gSinβ.

If α > β

So, g Sinα > g Sinβ

So, more the inclination of the plane more be the acceleration of body and hence the time taken is less.

So, the body kept on the inclined whose inclination is more reaches at the bottom first.

Answer 2

The mass sitting on the plane inclined to a greater angle to the horizontal will reach the bottom first because it will experience greater acceleration.

• Let the angle of inclination of the first mass to the horizontal = θ
• Let the angle of inclination of the second mass to the horizontal = β

The net horizontal force on the masses is calculated as follows;

$\Sigma F_x = 0\\\\mgsin(\theta) = ma\\\\gsin(\theta) = a\ \ \ or \ \ \ \\\\gsin(\beta ) = a$

Assuming the value of the angles of inclination of the plane is the following;

• θ = 60⁰   and  β = 30⁰

a = gsin(60) = 0.866g

a = gsin(30) = 0.5g

Thus, we can conclude that the mass sitting on the plane inclined to a greater angle to the horizontal will reach the bottom first because it will experience greater acceleration.

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