Question

true or false: when an acorn falls from a branch that is above the ground, assuming there is no air resistance, you are not required to know the mass of the acorn to calculate the velocity of the acorn as it strikes the ground.

Answer 1

In the absence of air resistance, the mass of an acorn does not affect its velocity as it falls. All objects experience the same acceleration due to gravity. So the statement is true.

True. In the absence of air resistance and other external forces, the mass of an object does not affect its acceleration due to gravity. All objects near the surface of the Earth, regardless of their mass, experience the same acceleration due to gravity, which is approximately 9.8 meters per second squared. This principle is known as the equivalence principle and was famously demonstrated by Galileo dropping different objects from the Leaning Tower of Pisa.

Therefore, when an acorn falls from a branch, its mass does not factor into the calculation of its velocity as it strikes the ground. The only relevant factors are the height from which it falls and the acceleration due to gravity. The equation to calculate the final velocity (v) of a falling object, neglecting air resistance, is given by:

`\[v = √(2gh)\]`

where:

-
`\(g\)` is the acceleration due to gravity (approximately 9.8 m/s² on the surface of the Earth),

`- \(h\)` is the height from which the acorn falls.

As you can see, the mass of the acorn is not present in this equation.