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Question

Suppose you are playing tug-of-war. Team A has $5$ members and team B has $5$ members. Assume the force applied by each person by giving a random magnitude of forces and discuss the resultant force. Now, assume that team B is reduced to $4$ members. Find out how much extra force each member of team B has to apply to compete with team A.

Accepted Answer

The resultant force is nothing but the total force acting on a body including its directions. All forces are acting in the same direction, resultant force should be the sum of all the forces. If the forces act in the opposite directions, the resultant force is obtained by taking the difference between the forces. The direction of the resultant force is along the direction of the force that has a greater magnitude.

Let the forces applied by each member be $100 N$ .

In the first case:

Given

Number of participants in team A $= 5$

The total force by team A $= 100 + 100 + 100 + 100 + 100 = 500 N$

Number of participants in team B $= 5$

The total force by team B $= 100 + 100 + 100 + 100 + 100 = 500 N$

Here, a force $500 N$ by team A is acting towards the left and another force by team B of $500 N$ towards the right. The resultant force will be $500 N - 500 N = 0 N$ . This is because both forces are equal and in opposite directions.

In the second case:

Given

Number of participants in team A $= 5$

The total force by team A $= 100 + 100 + 100 + 100 + 100 = 500 N$

Number of participants in team B $= 4$

The total force by team B $= 100 + 100 + 100 + 100 = 400 N$

Here, a force $500 N$ by team A is acting towards the left and another force by team B of $400 N$ towards the right.

To compete with team A, team B should apply $500 N$ .

$∴$ Total force each member of team B has to apply $= \frac{500}{4} = 125 N$ .

The force by team A members is $100 N$ .

Therefore, the extra force each member of team B has to apply to compete with team A is $125 - 100 = 25 N$ .

Subject Experts Solutions for Chapter: Force, Exercise 3: Challenge Yourself

Subject Experts Physics Solutions for Exercise - Subject Experts Solutions for Chapter: Force, Exercise 3: Challenge Yourself

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