In some problems, particles interact with other particles, causing their forces to interact. Particles connected together can be considered as separate particles or as one single particle if their motion is along a straight line. According to Newton's third law, any particle will exert an equal and opposite force to any force that acts on it.
Equations
DESCRIPTION
EQUATION
Newton's second law
F=ma
Variables
Quantity name
symbol
unit name
unit symbol
Force
F
Newton
N
Mass
m
Kilograms
kg
Acceleration
a
Metrespersecondsquared
ms−2
Tension
T
Newton
N
NormalForce
N
Newton
N
Newton's third law
Newton's third and final law of motion states that:
"For every action there is an equal and opposite reaction"
Consider a stationary object of mass m resting on a table.
The object experiences a weight force due to gravity, mg, which if unstopped would pull the object towards the Earth's core. It is halted by the table, which exerts an opposite reaction force, the normal force N. As this object is in equilibrium, these forces cancel out. Therefore:
N=mg
Connected particles
In some cases, particles will be operated on by multiple forces, and interact with multiple particles. In cases where connected particles are moving along one dimension, consider all connected objects as one object, and assume the forces affecting the multiple object affect this one object. You need to be able to think as connected particles as one single object or as many different parts depending on what you are trying to find.
Example 1
Two particles of mass 4kg and 6kg are joined by a light, inextensible string in the manner shown below. The 6kg block is pulled to the right with a force of 20N.
(i) What is the acceleration a felt by the particles?
(ii) What is the tension T in the string connecting the particles?
To find the acceleration, consider the two objects as one. As such, the masses add together and the tension forces T cancel each other out.
2F=maF=20m=4+6=100=10aa=2ms−2
To find the tension T, consider one particle by itself. Using the 6kg, find the tension:
FFma20−T20−T−TT=ma=20−T=6=2=6×2=12=12−20=8N
Verify the answer by using the 4kgparticle, as the tension force should be equal.
F=maF=Tm=4a=2T=4×2T=8N
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Contact and non-contact forces
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Newton's laws
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Connected particles
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FAQs - Frequently Asked Questions
How do you solve problems with connected particles?
Connected particles, if their motion occurs in a straight line, can be dealt with as one single whole. This simplifies the problem and allows you to be flexible in what you are trying to solve.
What forces act on stationary object on a table?
A weight acting vertically downwards and an equal opposite normal reaction force acting vertically upwards.
What is Newton's third law?
Newton's third law states that "For every action there is an equal and opposite reaction".