Page 101 -

Physics
Mechanical energy and the law of conservation of mechanical energy

Have you ever been on a rollercoaster ride? The
100 kg
cars slowly reach the required height and then E + E
K p
descend rapidly, dramatically increasing their Maximum height 20 m, E
speed. The kinetic energy of the cars changes 1 p
repeatedly, from maximum to minimum values
and back, due to the ever-changing speed. 2 15 m, E
textbooks nis edu kz
K
The same happens to the cars’ potential energy,
due to the changing height. If the energy spent 3
on overcoming friction is disregarded, then
the sum of the kinetic and potential energies
– mechanical energy – does not change.
This is a result of the law of conservation of
mechanical energy.

REMEMBER! Mechanical energy equals the sum of kinetic and potential energies.

ACT Calculate the mechanical energy of a rollercoaster car at every stage of motion and
the maximum speed of the car at the bottom.

Given Solution
m = 100 kg а. At maximum height (v = 0) potential energy is

h = 20 m E p = mgh = 100 kg · 10 m · 20 m = 20 000 J
s 2
h = 15 m
Mechanical energy at maximum altitude
g =10 m/s 2
E m = E k + Ep = 0 + 20 000 J = 20 000 J
Е = ?
М b. Mechanical energy of the car is also E m = 20 000 J at altitude of 15 m and at the bottom,
v = ? according to the law of mechanical energy conservation.

c. As there is no potential energy at the bottom (h = 0), all mechanical energy will be in
the form of maximum kinetic energy
2
mv
E m = E k = 20 000 J, as E k = , therefore v = 2E k = 20 m/s
2 m
Answer: Е = 20 000 J and = 20 m/s
m

INV Design an experiment to investigate the energy transfers on a ping-pong ball as you
drop it from different heights, and analyze energy transformations throughout its motion.

OVER TO YOU!

1. Describe the energy transfers of the water in a waterfall. Use the 3. If a car does not accelerate as
key words you have learnt. it approaches an uphill section
of road it will be difficult for
2. Would you dare to ride on the rollercoaster with the longest drop
it to reach the top of the hill.
in the world? Kingda Ka in the United States has a 127-metre
Explain why this is so, and give
vertical drop. Estimate its top speed at the bottom of the drop.
reasons for your answer using
What assumptions do you have to make for this calculation?
key words from the unit.
101