Question

A person drops a pebble of mass m1 from a height h, and it hits the floor with kinetic energy KE. The person drops another pebble of mass m2 from a height of 4h, and it hits the floor with the same kinetic energy KE. How do the masses of the pebbles compare

Answer 1

The mass of the first pebble (m1) is four times the mass of the second pebble (m2) because it was dropped from a height h and hit the floor with the same kinetic energy as the second pebble did from a height of 4h.

Step-by-step explanation:

When a person drops a pebble of mass m1 from a height h, it converts its gravitational potential energy into kinetic energy as it hits the floor. The kinetic energy (KE) can be calculated as KE = m1 * g * h, where g is the acceleration due to gravity. When a second pebble of mass m2 is dropped from four times the height (4h), and it hits the floor with the same kinetic energy, its initial potential energy was PE = m^2 * g * 4h. Since the kinetic energy is the same when both pebbles hit the floor, we set the equations equal to each other to compare the masses.

The kinetic energy for both pebbles is KE hence,

m1 * g * h = m2 * g * 4h

Cancelling out the common factors we get,

m1 = 4 * m2

This demonstrates that the mass m1 must be four times the mass of m2.

Answer 2

Hello,

QUESTION)

✔ We have: KE = PE (potential energy)

PE = m x g x h

The potential energy that the pebble of mass 1 has is called PE1 and the potential energy that the pebble of mass 2 has is called PE2

PE1 = PE2 ⇔ PE1/PE2 = 1

`(m_1* g* h)/(m_2* g* 4h) = 1 \\ \\ (m_1)/(m_2* 4) = 1 \\ \\ (m_1)/(m_2) = 4`

The mass m1 is therefore 4 times greater than that of the stone of mass m2.