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QA2:
Two persons manage to push a motorcar of mass 1200 kg at a uniform velocity along a level road. The same motorcar can be pushed by three persons to produce an acceleration of 0.2 $m s^{-2}$. With what force does each person push the motorcar? (Assume that all persons push the motorcar with the same muscular effort.)
Solution :
Step 1: Identifying Variables and Initial Conditions
Given data:
- Mass of the motorcar ($m$) = $1200\text{ kg}$
- Acceleration with three persons ($a$) = $0.2\text{ m s}^{-2}$
- Let the force exerted by one person be $F$.
- Let the frictional force opposing the motion be $f$.
[Per Newton's First Law of Motion, an object moving at a constant velocity implies that the net external force acting on the object is zero. Therefore, the force applied must be equal to the frictional force.]
Step 2: Analyzing the Two-Person Scenario
When two persons push the car at a uniform velocity, the total applied force equals the frictional force:
$2F - f = 0 \implies f = 2F$ [Equation 1]
Step 3: Analyzing the Three-Person Scenario
When three persons push the car, it produces an acceleration ($a$). [Per Newton's Second Law of Motion: $F_{net} = ma$]:
$3F - f = ma$ [Equation 2]
Step 4: Solving the System of Equations
Substitute Equation 1 into Equation 2:
$3F - (2F) = ma$
$F = ma$
Substitute the given values ($m = 1200\text{ kg}$, $a = 0.2\text{ m s}^{-2}$):
$F = 1200\text{ kg} \times 0.2\text{ m s}^{-2}$
$F = 240\text{ N}$
Visual Representation of Force Vectors
Step 5: Verification of Results
| Scenario | Applied Force | Net Force |
|---|---|---|
| 2 Persons | $2 \times 240 = 480\text{ N}$ | $480 - 480 = 0\text{ N}$ (Uniform Velocity) |
| 3 Persons | $3 \times 240 = 720\text{ N}$ | $720 - 480 = 240\text{ N}$ ($F=ma$ holds: $1200 \times 0.2 = 240$) |
Final Solution: Each person pushes the motorcar with a force of 240 N.
More Questions from Class 9 Science Force and Laws of Motion Additional Exercises
- QA1(a): The following is the distance-time table of an object in motion: (a) What conclusion can you draw about the acceleration? Is it constant, increasing, decreasing, or zero?
- QA1(b): The following is the distance-time table of an object in motion: (b) What do you infer about the forces acting on the object?
- QA3: A hammer of mass 500 g, moving at 50 $m s^{-1}$, strikes a nail. The nail stops the hammer in a very short time of 0.01 s. What is the force of the nail on the hammer?
- QA4: A motorcar of mass 1200 kg is moving along a straight line with a uniform velocity of 90 km/h. Its velocity is slowed down to 18 km/h in 4 s by an unbalanced external force. Calculate the acceleration and change in momentum. Also calculate the magnitude of the force required.
CBSE Solutions for Class 9 Science Force and Laws of Motion
Chapters in CBSE - Class 9 Science
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