Muskan Shafi Education Content Expert
Education Content Expert
Average Force is the force exerted by an object that is moving at a certain velocity during a given period of time.
- It is the mass of the body multiplied by the average velocity over a definite time.
- It is a vector quantity as it has both magnitude and direction.
- The word ‘Average’ is used to denote that the velocity is not an instantaneous or precisely measured velocity.
- At times, multiple forces may be applied to a single object, thus, the average force is calculated in such situations.
Average Force Formula helps to find out the rate of change of momentum for any number of time intervals. Average Force Formula is given as
| \(F = \frac{m (V_f-V_i)}{\Delta t}\) |
Here, m denotes the mass of the object, t denotes time taken, and vi and vf refer to the initial and final velocity of the object respectively.
Read More: Force and Motion
Key Terms: Average Force Formula, Force, Velocity, Speed, Momentum, Vector, Magnitude, Average Force, Newton, Average Velocity
What is Average Force?
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Average Force is the force generated by an object moving at a defined rate of speed, i.e. velocity for a given period of time.
- Average Force is a quantity that has both magnitude and direction, thus, it is a vector quantity.
- The term ‘average’ implies that average force is not a constant or precisely measured velocity.
- Average force is equal to the product of the mass and the average velocity of the object over the defined time.
- Average Force is expressed in Newton (N).
Average Force
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Average Force Formula
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Average Force is equal to the mass of the object multiplied by the average velocity of the object during the given duration. For a particular period of time t, the force will be the periodicity of momentum change. In case there are several time intervals, the average force is the rate of variation of momentum.
Mathematically, the Average Force Formula is given as
| \(F = \frac{m (V_f-V_i)}{\Delta t}\) |
Where
- F is the Average Force.
- m is the mass of the object.
- Vf is the final velocity.
- Vi is the initial velocity.
- Δt is the time or change in time.
Average Force Formula
Read More: Balanced Force
Solved ExampleExample: A boy throws a shot-put ball with a mass of 7 kg and it rolls with a velocity of 4 m/s for 2 s. Calculate the average force. Solution: Given parameters are:
Using the Average Force Formula, \(F = \frac{m (V_f-V_i)}{\Delta t}\) F = [7(4-0)]/2 = (7 x 4)/2 F = 28/2 = 14 Thus, the average force is 14 N. |
Solved Examples on Average Force Formula
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Given below are a few solved examples on the Average Force Formula to understand the concept better:
Example 1: A ball of mass 4 kg is rolled at 6 m/s for a time duration of 12 seconds. What will be its average force?
Solution: According to the question,
- Mass of Ball (m) = 4 Kg
- Initial Velocity (vi) = 0
- Final Velocity (vf) = 6 m/s
- Time (t) = 12 seconds
Using the Average Force Formula,
\(F = \frac{m (V_f-V_i)}{\Delta t}\)
F = [4(6-0)]/12 = (4 x 6)/12
F = 24/12 = 2
Thus, the average force is 2 N.
Example 2: A car of mass 600 kg travels at a speed of 20 m/s in 5 seconds. Calculate the average force.
Solution: Given parameters are:
- Mass (m) = 600 kg
- Initial Velocity (Vi) = 0 m/s
- Final Velocity (Vf) = 20 m/s
- Time (t) = 5 s
Using the Average Force Formula,
\(F = \frac{m (V_f-V_i)}{\Delta t}\)
F = [600 (20 – 0)]/5
F = [600 x 20]/5 = 12000/5 = 2400 N.
Thus, the average force is 2400 N.
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Things to Remember
- Force is defined as a push or a pull that can change the motion of an object.
- Average Force is the force exerted by an object moving at a specific velocity during a given period of time.
- It is a vector quantity with both magnitude and direction.
- Average Force is not a constant or absolutely measured value for velocity.
- It is the product of mass and average velocity during the given duration.
- Average Force Formula is \(F = \frac{m (V_f-V_i)}{\Delta t}\), where m is the mass, t is the time taken, and vi and vf are the initial and final velocities.
Previous Years’ Questions
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Sample Questions
Ques. Calculate the average force on an object of mass of 4 kg, if it rolled at 6 m/s for 3 seconds. (3 Marks)
Ans. Given parameters are
- Mass of Object (m) = 4 kg
- Initial Velocity (Vi) = 0 m/s
- Final Velocity (Vf) = 6 m/s
- Time (t) = 5 s
Using the Average Force Formula,
F = m (vf – vi)/Δ t
F = [4 (6 – 0)]/3
F = [4 x 6]/3 = 24/3 = 8 N.
Thus, the average force on the object is 8 N.
Ques. A dog with a weight of 10 kg chases a bike with a velocity of 5 m/s for 12 seconds. What will be the average force? (3 Marks)
Ans. Given that,
- Mass of Dog (m)= 10 Kg
- Average velocity of Dog = 5 m per s
- Time (t) = 12 seconds
Using the Average Force Formula,
F = m (vf – vi)/Δ t
F = [10 (5 – 0)]/12
F = [10 x 5]/12 = 50/12 = 4.166 N.
The average force on the dog is 4.166 N.
Ques. A child throws a bowling ball of 5 kg that rolls with a velocity of 4 m/s for 2 seconds. What will be the average force applied? (3 Marks)
Ans. Given that,
- Mass of Ball (m) = 5 Kg
- Initial Velocity (Vi) = 0 m/s
- Final Velocity (Vf) = 4 m/s
- Time (t) = 2 s
Using the Average Force Formula,
F = m (vf – vi)/Δ t
F = [5 (4 – 0)]/2
F = [5 x 4]/2 = 20/2 = 10 N.
Thus, the average force applied is 10 N.
Ques. What is Net Force? What is Net Force Formula? (3 Marks)
Ans. There is a certain net force that is applicable to all objects. Net Force is the vector sum total of all forces that are acting on an object. According to Newton’s second law, if there is a net force acting on any particular object, that object is accelerating, so the speed of the object will change with every second.
If a number of forces are acting on a body, the Net Force Formula is given as
FNet = F1 + F2 + F3…. + FN
Where F1, F2, F3…FN are the forces acting on the body.
Ques. A dog weighing 20 kg chases a person for 16 seconds with a velocity of 7 m/s. What will be the average force for the dog? (3 Marks)
Ans. According to the question,
- Mass of the Dog (m) = 20 kg
- Average Velocity = 7 m/s
- Time (t) =16 seconds
Using the Average Force Formula,
F = m (vf – vi)/Δ t
F = [20(7-0)]/16
F = (20 x 7)/16
F = 140/16 = 8.75 N
Thus, the average force of the dog is 8.75 N.
Ques. A player throws a bowling ball of mass 5 kg which rolls with a velocity of 4 m/s for 1 s. Calculate its average force. (3 Marks)
Ans. According to the question,
- Mass of Bowling Ball (m) = 5 Kg
- Initial Velocity (vi) = 0 m/s
- Final Velocity (vf) = 4 m/s
- Time (t) = 1 s
Using the Average Force Formula,
F = m (vf – vi)/Δ t
F = 5(4-0)/1
F= 20 N
Therefore, the average force is calculated as 20 N.
Ques. A tennis ball of a mass of 0.25 kg rolls over the gravel with a velocity of 1.5 m/s for 2 s. What will be its average force? (3 Marks)
Ans. Given parameters are
- Mass of Ball (m) = 0.25 kg
- Initial Velocity (vi) = 0 m/s
- Final Velocity (vf) = 1.5 m/s
- Time (t) = 2s
Using the Average Force Formula,
F = m (vf – vi)/Δ t
F= 0.25 (1.5 – 0)/2 = 0.1875 N
F= 0.1875 N
Therefore, the average force is calculated as 0.1875 N.
Ques. What is Average Force? (2 Marks)
Ans. Average Force refers to the force that is generated by an object moving at a defined rate of speed for a defined span of time. It means that the force measured here is not instantaneous or precisely measured velocity. It is expressed in terms of the unit Newton (N).
Ques. What will be the average force on an object of mass of 70 kg, if it rolled at 8 m/s for 8 seconds? (3 Marks)
Ans. Given that,
- Mass of Object (m) = 70 kg
- Initial Velocity (Vi) = 0 m/s
- Final Velocity (Vf) = 8 m/s
- Time (t) = 8 s
Using the Average Force Formula,
F = m (vf – vi)/Δ t
F = [70 (8 – 0)]/8
F = 56/8 = 7 N.
Thus, the average force on the object is 7 N.
Ques. What is Force? Why do we calculate average force? (2 Marks)
Ans. Force refers to a push or a pull on an object when it is in contact with another object. During such an interaction, a force is exerted on both objects. At times, multiple forces may be applied to a single object. Thus, in such a situation, the average force is calculated.
Ques. Are average force and net force the same thing? (2 Marks)
Ans. Average force refers to the force that is variable and is not constant over time. It lays out a more or less uniform value to calculate the other aspects associated with it. Whereas, on the other hand, net force refers to the total force applied to the object.
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