Question

A stone of mass 64.0 g is thrown vertically upward from the ground with an initial speed of 20.0 m/s. The gravitational potential energy at the ground level is considered to be zero. Apply the principle of conservation of energy and calculate the potential energy at the maximum height attained by the stone (g = 10 m s⁻²).

Answer 1

Given Data:

Mass of the stone (m) = 64.0 g = `64.0/1000` kg = 0.064 kg

Initial speed at the ground (u) = 20.0 m/s

Acceleration due to gravity (g) = 10 m/s²

According to the Principle of Conservation of Energy, the total mechanical energy remains constant throughout the motion.

Total Energy at the Ground = Total Energy at Maximum Height

1. Calculate Total Energy at Ground Level:

Potential Energy at the ground `("PE"_("ground"))` = 0 J (Given)

Kinetic Energy at the ground:

`"KE"_("ground") = 1/2 xx m xx u^2`

= `1/2 xx 0.064  kg xx (20)^2`

= 0.032 × 400

= 12.8 J

Total Energy at Ground = PE + KE

= 0 + 12.8

= 12.8 J

2. Calculate Potential Energy at Maximum Height:

At the highest point, the stone momentarily comes to rest, so its final velocity becomes zero (v = 0).

Kinetic Energy at maximum height (KE_max) = 0 J

By conservation of energy:

Total Energy at Maximum Height = Total Energy at Ground

PE_max + KE_max = 12.8 J

PE_max + 0 = 12.8 J

PE_max = 12.8 J

The potential energy at the maximum height attained by the stone is 12.8 J.