Work Energy Power

Question 1

What is the basic formula for work done if force is constant?

Answer 1

For constant force,
W = F⃗.s⃗
or
W = F⃗.(r⃗₂-r⃗₁)

Question 2

What is the formula for work done if force F(x) varies with distance?

Answer 2

For variable force dependent on displacement F(x),
W =∫ F(x).dx

Question 3

How do you derive work from a F Vs Displacement graph?

Answer 3

Work is Area under the F Vs Displacement graph.

Question 4

What is the formula for work done if force varies with time? Derive the same

Answer 4

For variable force dependent on time F(t),
W =∫ m.a(t) X f(t).dt
a(t) = F(t) / m
Integrating above we get,
v = f(t) –> not sure how
⇒ dx = f(t).dt
⇒ W =∫ m.a(t) X f(t).dt

Question 5

State the different types of forces that cause work to be done?

Answer 5

Work can be done due to various forces
1. Conservative Forces (e.g Gravitational, Electrostatic and Spring Force)
2. Non- conservative Forces (e.g Friction and Viscous force)
3. External Agent (e.g a person applying a force)
4. Tension in String or the Normal Force

Question 6

What is the Work Energy Theorem.

Answer 6

Net Work Done = Change in Kinetics Energy,
W_net = K_f-K_i = ΔK

Question 7

Express the Work Energy theorem as a sum of the work done by various types of forces.

Answer 7

W_Conservative+W_{Non-Conservative}
+W_{ext</sub = ΔK}

Question 8

Express work energy theorem as a function of change in K.E and P.E

Answer 8

In W_Conservative+W_{Non-Conservative}
+W_{ext</sub = ΔK,
WConservative is nothing but change in P.E and hence can be written as
-ΔU+WNon-Conservative
+Wext</sub = ΔK,
Re-arranging we get,
WNon-Conservative
+Wext</sub = ΔK + ΔU}

Question 9

Mathematically, what is Total Change in Mechanical Energy

Answer 9

ΔK + ΔU is Total change in Mechanical Energy

Question 10

What is Law of Conservation of Energy? Express mathematically.

Answer 10

In the absence of non-conservative or external force, or their work done is zero, then total change in mechanical energy is zero.

ΔK + ΔU = 0,
K_f-K_i+U_f-U_i = 0
K_i+U_i = K_f+U_f