You are here
A moving bicycle, a rolling ball — all moving things can do work. How much energy does motion carry, and how does it depend on speed?
- The energy an object has due to its motion is its kinetic energy . A motionless object has zero kinetic energy.
- For a constant force on mass m , using v 2 = u 2 + 2as and W = F× s = ma× s : W = 1 2 m(v 2 - u 2 )
- By the work-energy theorem this is the change in energy. Starting from rest ( u = 0 ), the kinetic energy of an object of mass m moving at velocity v is K = 1 2 mv 2
- KE has no direction and its unit is the joule (J). It increases with positive work (speeding up) and decreases with negative work (slowing down).
- Kinetic energy — the energy possessed by an object due to its motion; for mass m at velocity v, K = ½mv².
If a vehicle's velocity doubles, how does its kinetic energy change?
Initial
K =
1
2
mv
2
. At
2v
:
K'
=
1
2
m(2v)
2
= 4 ×
1
2
mv
2
.
The kinetic energy becomes 4 times the original value.
A cricket ball of mass 0.2 kg is bowled at about 154.8 km h⁻¹. Find its kinetic energy.
v
= 154.8
km h
-1
= 43
m s
-1
.
K
=
1
2
mv
2
=
1
2
× 0.2 × 43
2
= 184.9
J
.
A 15000 kg jet is stopped within 100 m by a wire exerting 367500 N. Find its velocity just before the hook caught.
Change in KE = work done by the wire (force opposes motion, so work is negative):
0 -
1
2
× 15000 × v
2
= -(367500 × 100)
v
2
=
367500 × 2 × 100
15000
= 4900
⇒ v
= 70
m s
-1
= 252
km h
-1
towards the carrier.
-
4. A (mass m) and B (mass 4m) have equal KE — ratio of velocities?
1
2
m v
A
2
= 1 2 (4m)v B 2
⇒ v A 2
= 4 v B 2
⇒ v A : v B
= 2 : 1 . - 5. Does KE of an object at constant velocity change with position? No — kinetic energy depends only on mass and speed, so at constant velocity it stays the same wherever the object is.
NCERT Question 8 — A man of mass 60
A man of mass 60 kg rides a scooter of mass 100 kg. He accelerates the scooter to a velocity v. The next day, his son with a mass of 40 kg joins him as a passenger. If the scooter reaches the same speed on both days in the same time interval, what is the ratio of the fuel of the tank used on the two days? Assume that the energy transfer to the scooter happens entirely due to fuel, and no other losses occur due to air resistance and friction.
NCERT Question 11 — A 10.0 kg block is
A 10.0 kg block is moving on horizontal floor with negligible friction. As shown in Fig. 7.37, a variable force is applied on the block in its direction of motion from its position at 0 m till 4 m. If the block had a kinetic energy of 180 J when it was at 0 m, find the block's speed (i) at 0 m, and (ii) at 4 m. Does the block have negative acceleration in any portion of its motion?
NCERT Question 13 — A 1000 kg car is
A 1000 kg car is moving along a road at a constant speed. Suddenly, the driver notices some obstruction ahead and applies the brakes to come to a complete stop. The graphical representation of motion of the car (Fig. 7.38) starts from the instant the driver spots the traffic. (i) Describe how the car moves between positions A and B. (ii) Calculate the kinetic energy of the car at A. (iii) State the work done by the brakes in bringing the car to a halt between B and C. (iv) What does the kinetic energy of the car transform into?
