Force - Definition, Effects, Types, Sample Problems
Last Updated : 21 Apr, 2025
In everyday life, we often notice that some effort is required to set an object in motion or to bring a moving object to a stop. This effort is experienced as a muscular force, where we push, pull, or hit the object to change its state of motion. Therefore, Force can be defined as a push, pull, or impact that causes a change in an object's motion. It is exerted by one object on another, influencing its speed, direction, or shape.
e.g:, When a box is pushed, it moves forward and changes its state of motion, hence, we can say that when a force was applied to the box in the form of a push, it changed its state from rest to motion.
A force is being applied to the box in the form of a pushForce can also change the shape and size of any object. The greater the force is applied, the more the changes will be observed in the shape and size of any object.
e.g:, When a force is applied to a spherical rubber ball, it changes its shape from spherical to oblong.
Due to the application of force, the shape of a ball got changedIn this way, the force has many applications in our everyday lives such as the force due to one's foot pushing on the pedal when riding a bicycle, the force applied of the bat by the ball. A general case for the existence of the normal force is when a person stands on the ground i.e. the ground exerts a force on the person that is equal in magnitude to the person’s weight.
Effects of Force
From the above examples, various effects of force can be summed as below:
- It can change the state of motion of a body.
- It can change the direction of the moving body.
- It can change the size or shape of a body.
- It can accelerate the speed of the moving body.
- It can slow down the speed of the moving body.
Types of Forces
There are two types of Forces depending upon whether the effect of force is seen or felt or not. These are as follows:
1) Balanced force
2) Unbalanced force
1. Balanced Force
The equal and opposite force acting on an object that does not change the state of rest or of motion of that object is known as the Balanced force.
The forces acting on an object are said to be balanced (or if there are no forces acting on it) when the object is not moving stays still or the object which is moving continuously with the same speed and in the same direction. Therefore, the types of forces in which the resultant of all the forces acting on the object is zero are known as balanced forces.
e.g.:, When a wooden block is kept on a table and equal forces are applied on both sides of the block then the block will not move in any direction.
Balanced forces acting on the blockClearly, the forces are balanced as a force of 120 N is applied to the left of the block as well as to the right of the block. The net force acting on the box must be equal to the difference between the two forces F1 and F2:
F = F1 - F2 = 120 N - 120 N = 0 N.
Since the resultant/net force is zero hence, the block will not change its state of rest.
Another example can be of a box placed on the rough surface, So if the box is pushed with a small force, the box do not change its position or remains at rest due to the frictional force acting in a direction opposite to the push it. This means the box balances the pushing force acting on it with the frictional force between the box and surface, of the same amount and therefore the box does not move.
2. Unbalanced Forces
The unequal and opposite force acting on an object, that tends to move the object in the direction of larger force applied is known as the unbalanced force.
The forces acting on an object are said to be unbalanced forces when the net force on the object is not zero. When the net forces acting on then the object results in an unbalanced force, then due to which the force accelerates the object. This means that a net force acting on the object can either change the direction or magnitude of its velocity.
e.g.:, Consider the same case of the box as described in balanced force, with a difference that the two forces applied are of different magnitudes on the opposite sides of the block, so the block moves in the direction of the larger force.
Unbalanced forces acting on the blockClearly, the forces are unbalanced as a force of 120 N is applied to the left of the block while a force of 60 N is applied to the right of the block.
The net force acting on the box must be equal to the difference between the two forces F1 and F2:
F = F1 - F2 = 120 N - 60 N = 60 N.
Since F1 is the greater force hence, the block will move in the direction of F1.
So, it is concluded that an object moves with a constant speed when all the forces acting on the object are balanced and there is no net external force acting on it.
When an unbalanced force is applied to the object, there will be a change either in its speed or in the direction of its motion.
Thus, to accelerate the motion of an object, an unbalanced force is required. And the change in its speed (or in the direction of motion) would continue as long as this unbalanced force is applied.
Units of Force
Since force has both magnitude and direction, it is considered a vector quantity. The direction of the force is represented by an arrow, while the magnitude is measured using specific units. The standard unit of force is the Newton (N), where 1 Newton is the force required to accelerate a 1-kilogram mass by 1 meter per second squared.
Note: In the SI base unit, Newton is equivalent to Kg m/s2
Representation of Force
Force is denoted by the symbol (F). The quantity of force can be expressed by the vector product of mass (m) and acceleration (a). So the mathematical representation of the force can be written as follows:
F = m × a
where, F is the force, m is the mass of the object and a is the acceleration obtained.
Now, since acceleration is the change in the velocity of the moving body, hence other mathematical representation of the force can be written as follows:
F = m × a
Since,
a = (v-u)/t
So,
F = m × (v-u)/t
where, u and v are the initial and final velocities respectively and t is the time taken.
Sample Problems
Problem 1: Suppose one have a box of mass 2 kg. How much force should be applied to the box so that it should travel with the acceleration of 8 m/s2?
Solution:
Given that,
The mass of the box, m = 2 kg and
The acceleration of the box a = 8m/s2.
The formula to calculate the force is:
F = m × a
So on putting the value of 'm' and 'a' in the above equation as:
F = 2 kg × 8 m/s2
= 16 kg m/s2 or 16 N.
Problem 2: A ball of mass 2 kg is moving with the initial speed of 5 m/s and then suddenly comes to rest in 0.02 sec. Calculate the force that changed the state of the moving ball.
Solution:
To calculate the force that changed the state of the moving ball, we can use Newton's second law of motion, which states that the force (F) acting on an object is equal to the rate of change of momentum (Δp) can be expressed as
F = Δp /Δt
Given :
mass (m) = 2kg , initial speed (u) = 5m/s , final speed(v) = 0m/s , change in time (Δt) = 0.02sec
The change in momentum (Δp) can be calculated as the difference between the final momentum (mv) and the initial momentum(mu).
Δp = mv-mu
Δp = m(v-u)
Δp = 2(0-5)
Δp = -10kg m/s
Now, we can calculate the force using the formula:
F = Δp / Δt
F = -10 / 0.02
F = -500 N
The negative sign indicates that the force is acting in the opposite direction of the initial velocity, causing the ball to come to rest. Therefore, the force that changed the state of the moving ball is 500N in the direction opposite to its initial motion.
Problem 3: If a block is placed on a wooden table such that on one side of the block, a force of 100 N is being applied, and on the other side, a force of 40 N is being applied. Will the block move? If yes, then specify the magnitude of the force and the direction of the force.
Solution:
Given that,
The force applied from one side of the block, F1 = 100 N and
The force applied from the other side of the block, F2 = 40 N.
The resultant force can be calculated as the difference between the two forces, which is:
100 N - 40 N = 60 N.
Since the resultant force is not zero, hence the block will surely move in the direction of F1 as F1 is a larger force in comparison to F2.
Problem 4: A 13 kg block slides along the floor with a constant velocity. What is the net force on the block?
Solution:
Given that,
The mass of the block, m = 13 kg.
Since the block is sliding with a constant velocity, so net acceleration will be zero i.e. a = 0 m/s2.
The formula to calculate the force is:
F = m × a
Put all the given values in the above expression to calculate the force.
F = 13 × 0 m/s2 = 0 N.
Problem 5. The two balls with masses as 10 kg and 20 kg respectively. Their respective accelerations are 20 m/s2 and 40 m/s2. Find the ratio of their respective forces.
Solution:
The mass of the first ball, m1 = 10 kg.
The mass of the second ball, m2 = 20 kg.
The acceleration of the first ball, a1 = 20 m/s2.
The acceleration of the second ball, a2 = 40 m/s2.
Using the formulae:
F1 = m1 × a1 and
F2 = m2 × a2
Therefore,
F1 = 10 kg x 20 m/s2 = 200 N
Similarly,
F2 = 20 kg x 40 m/s2 = 800 N
Hence,
F1 : F2 = 200 N : 800 N = 1 : 4.
Problem 6. Two objects have masses of 15 kg and 30 kg, respectively. Their respective accelerations are 10 m/s² and 25 m/s². Find the ratio of the forces acting on them.
Solution:
The mass of the first object, m1 = 15 kg.
The mass of the second object, m2 = 30 kg.
The acceleration of the first object, a1 = 10 m/s².
The acceleration of the second object, a2 = 25 m/s².
Using the formulas:
F1 = m1 × a1 and
F2 = m2 × a2
Thus,
F1 = 15 kg × 10 m/s² = 150 N
F2 = 30 kg × 25 m/s² = 750 N
Therefore,
F1 : F2 = 150 N : 750 N = 1 : 5.
Problem 7. A car with a mass of 1200 kg and a truck with a mass of 3000 kg are both accelerated at 5 m/s² and 2 m/s², respectively. Find the ratio of the forces acting on the car and the truck.
Solution:
The mass of the car, m1 = 1200 kg.
The mass of the truck, m2 = 3000 kg.
The acceleration of the car, a1 = 5 m/s².
The acceleration of the truck, a2 = 2 m/s².
Using the formulas:
F1 = m1 × a1 and
F2 = m2 × a2
Thus,
F1 = 1200 kg × 5 m/s² = 6000 N
F2 = 3000 kg × 2 m/s² = 6000 N
Therefore,
F1 : F2 = 6000 N : 6000 N = 1 : 1.
Problem 8. A 25 kg box is moving along a horizontal surface with a constant velocity. What is the net force acting on the box?
Solution:
Given that,
The mass of the box, m = 25 kg.
Since the box is moving with a constant velocity, the net acceleration is zero, i.e., a = 0 m/s².
The formula to calculate the force is:
F = m × a
Substituting the given values into the formula:
F = 25 × 0 m/s² = 0 N.
Therefore, the net force on the box is 0 N.
Conclusion
In conclusion, Force is a key factor that causes changes in an object’s motion or shape. It has both magnitude and direction and can be applied through pushing, pulling, or hitting. Force is present in everyday activities and plays an important role in areas like engineering and mechanics. It drives motion, alters directions, and can change the shape of objects.
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