Question

A boy throws a ball of mass 0.5 kg upwards with an initial speed of 14 m/s. The ball reaches a
maximum height of 8m. The amount of energy dissipated by air drag acting on the ball during
the ascent is then,
A. $4.9{\rm{ J}}$
B. $9.8{\rm{ J}}$
C. ${\rm{0 J}}$
D. ${\rm{13}}{\rm{.8 J}}$

Answer 1

Hint: First, the equation of motion with respect to the gravitational force constant g has to be
used to find the maximum height the ball can achieve when thrown upwards. The loss of energy
can be calculated by finding the difference between the maximum height and the attained height.
Given,
Mass of the chain is .
Initial speed is$u = 14{\rm{ m/s}}$.
The maximum height the ball reaches, $h = 8{\rm{ m}}$
The gravitational constant, $g = 9.8{\rm{ m/s}}$
The equation of motion due to gravity is given as,
$H = \dfrac{{{u^2}}}{{2g}}$ ……(1)
The equation of energy is given as,
$E = mgh$ ……(2)
If there is no air friction of drag of air, then the ball can reach a maximum height of,
$H = \dfrac{{{u^2}}}{{2g}} = \dfrac{{{{14}^2}}}{{2 \times 9.8}} = 10{\rm{ m}}$
But it is given that the maximum height it can achieve is $h = 8{\rm{ m}}$
Hence, the loss in energy can be calculated as,
$E = mg(H - h)$……(3)
Substituting the value of h as and the value of H as ${\rm{10 m}}$in equation (3), we get
$E = mg(H - h) = 0.5 \times 9.8(10 - 8) = 9.8{\rm{ J}}$
The loss in energy is calculated as $9.8{\rm{ J}}$
Hence, the correct answer is (B).
Note: In the solution, the student can use the concept of laws of motion due to gravity. The
energy is dependent on the mass, gravitational constant and the height from which the object is
dropped.