Question

An apple of mass 250 gram falls from a tree through a vertical distance of 6 m and reaches the ground at a velocity 8m/s if it experiences a constant air resistance during it's fall then the magnitude of workdone by air resistance on it is (g=10m/s2

Answer 1

Given : An apple of mass 250 gram falls from a tree through a vertical distance of 6 m and reaches the ground with a velocity 8 m/s.

it experiences a constant air resistance during its fall,  

To Find :  the magnitude of work done by the air resistance on it is (g = 10 m/s²) ​

Solution:

Change in potential Energy  = mgΔh  

m = 250 g = 1/4  kg

g = 10 m/s²

Δh =  - 6 m

Decrease in potential energy = (1/4)(10)(6)  = 15 joule

KE = (1/2)mv²

Increase in kinetic Energy  = (1/2(1/4)(8)² -  (1/2)(1/4)(0)²

= 8 Joule

Net Decrease in Energy  =  15 - 8  = 7 joule

Hence the magnitude of work done by the air resistance on it = 7 joule

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Answer 2

Given:

An apple of mass 250 gram falls from a tree through a vertical distance of 6 m and reaches the ground at a velocity 8m/s.

To find:

Work done by air resistance ?

Calculation:

• In this type of questions, always try to follow the method using WORK-ENERGY THEOREM.

• The theorem states that : the work done by all the forces on an object will be equal to the change in kinetic energy.

$W_{g} + W_{f}=\Delta KE$

$\implies \: mgh + W_{f} = \dfrac{1}{2} m {v}^{2} - 0$

$\implies \: (0.25 \times 10 \times 6) + W_{f} = \dfrac{1}{2} (0.25){8}^{2}$

$\implies \: 15+ W_{f} = 8$

$\implies \: W_{f} = - 7 \: joule$

So, magnitude of work done by air resistance is 7 Joule.