# Application of Newton's 2nd Law

```REAL LIFE APPLICATIONS OF NEWTON’S
1. Riding in an elevator:
2. Launching a rocket
ND
2
LAW
LET’S GO FOR A RIDE
Riding in an elevator:
The natural experiences you have while riding in an elevator can be explained by
Newton’s second law of motion.
Four(4) scenarios can play out when you are in an elevator:
1. When the elevator is at rest (a = 0m/s&sup2;)
2. When the elevator is accelerating upwards (a ≠ 0m/s&sup2;)
3. When the elevator is going up or down at constant velocity ((a = 0m/s&sup2;)
4. When the elevator is accelerating downwards (a ≠ 0m/s&sup2;)
THE ELEVATOR IS AT REST
When in a stationary elevator: the elevator is not going up or down, It is at rest.
Acceleration = 0m/s&sup2;
Let FN = Normal force and mg = weight force,
ƩF= FN - mg
ƩF = ma (Newton’s 2nd law of motion)
Therefore ƩF = FN - mg = ma
Since a = 0m/s&sup2;
ƩF = FN - mg = m(0)
ƩF = FN - mg = 0
FN - mg = 0
FN = mg
So, if the elevator is stationary, the normal force on you equals your actual
weight.
WHEN THE ELEVATOR IS ACCELERATING UPWARDS
Second Scenario:
When the elevator is speeding up, its acceleration is not zero like in the first case.
ƩF = ma (Newton’s 2nd law of motion)
ƩF = FN - mg = ma, (a ≠ 0m/s&sup2;)
FN - mg = ma
FN = mg + ma
So, the scale will show a reading greater than your weight force and you will feel
heavier than you actually are. This extra weight represent the force the additional
force the elevator must have to be able to overcome your weight and still move
you upward.
WHEN THE ELEVATOR IS MOVING WITH CONSTANT VELOCITY
THIRD SCENARIO:
When the elevator moves with constant velocity, this means the elevator is not
accelerating. So, acceleration is zero.
Regardless of whether the elevator is going up or down, (a = 0m/s&sup2;).
ƩF = ma (Newton’s 2nd law of motion)
ƩF = FN - mg = ma,
But (a = 0m/s&sup2;)
ƩF = FN - mg = m(0)
ƩF = FN - mg = 0
ƩF = 0, FN - mg
FN = mg.
Again, normal force equals your weight force.
WHEN THE ELEVATOR IS ACCELERATING DOWNWARD
FOURTH SCENARIO:
When the elevator accelerates downwards, (a ≠ 0m/s&sup2;)
ƩF = ma (Newton’s 2nd law of motion)
ƩF = FN - mg = ma, (a ≠ 0m/s&sup2;)
The downward acceleration of the elevator is negative. So, a = -a(m/s&sup2;)
ƩF = FN - mg = m(-a)
ƩF = FN - mg = -ma
FN - mg = -ma
FN =mg – ma
As the elevator slows down to complete stop, the reading on the scale becomes
less than your actual weight force. At this point your feel lighter than you actually
are.
SUMMARY OF NATURAL EXPERIENCE IN THE ELEVATOR
1.
2.
3.
4.
When the elevator is at rest: FN = mg
When the elevator is accelerating upwards: FN = mg + ma
when the elevator is going up or down at constant velocity: FN = mg
When the elevator is accelerating downwards: FN = mg - ma
1. Newton’s second law of motion can be defined as:
_________________________________________________________________
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1. ƩF = ma represent the _________ force on an object which can be balanced
or unbalanced
3. According to newton’s second law of motion, acceleration is net force(N) per
unit mass(kg)
a. True b. False
4.One of the following equation represents the force experience in an elevator
when the elevator a person is in an elevator going up or down at constant
velocity
a. FN = mg
b. FN = mg + ma
c. FN = mg - ma
```