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How Forces Affect Motion

🎓 Class 9📖 Science📖 8 notes🧠 15 Q&A⏱️ ~12 min

How Forces Affect MotionStudy Notes

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The Concept of Force

Explanation

The Concept of Force

Force is a fundamental concept in physics that explains how objects start moving, change their speed or direction, or even change shape. A force can be thought of as a push or pull acting upon an object resulting from the object's interaction with another object. For example, when a ball at rest is kicked, the force applied by the foot causes the ball to move. Similarly, a cricket bat striking a ball changes the ball's direction and speed. Even non-motion effects such as squeezing a lemon involve forces changing the shape of the lemon. Importantly, force is a vector quantity, meaning it has both magnitude and direction. This directional aspect is crucial because the effect of a force depends not only on how strong it is but also on the direction in which it acts. Forces can arise from contact interactions, like friction or tension, or from non-contact interactions, such as gravitational, magnetic, or electrostatic forces. The SI unit of force is the newton (N), named after Sir Isaac Newton, and it quantifies the strength of the force. One newton is the force required to accelerate a 1 kg mass by 1 m/s². When describing forces, it is essential to specify both magnitude and direction to fully understand their effects on objects. Changes in either magnitude or direction of a force can alter the resulting motion or deformation of an object. Measuring force is commonly done using a spring balance, which operates on the principle of Hooke's law. The spring inside the balance stretches proportionally to the force applied, allowing the magnitude of the force to be read from a calibrated scale. This method can measure various forces, including weight, tension, and applied pushes or pulls. Forces encountered in everyday life range widely in magnitude, from very small forces like a gentle touch (on the order of millinewtons, 10⁻³ N) to extremely tiny forces measured in scientific experiments (down to yoctonewtons, 10⁻²⁴ N). Understanding force is foundational to studying motion and forms the basis for Newton's laws of motion, which describe how forces influence the movement of objects.

  • Force is a push or pull that can cause motion or deformation of an object.
  • Force is a vector quantity, having both magnitude and direction.
  • The SI unit of force is the newton (N).
  • Forces can be contact (friction, tension) or non-contact (gravitational, magnetic).
  • Spring balances measure force magnitude based on spring extension.
  • Changing magnitude or direction of force changes its effect on an object.
  • 📌 Force: A push or pull on an object that can cause motion or deformation.
  • 📌 Newton (N): SI unit of force, equal to the force required to accelerate 1 kg mass by 1 m/s².
  • 📌 Vector quantity: A physical quantity having both magnitude and direction.

Balanced and Unbalanced Forces

Explanation

Balanced and Unbalanced Forces

In real-world situations, objects are rarely subjected to a single force; usually, multiple forces act simultaneously. The combined effect of these forces determines the motion of the object. When two or more forces act on an object, their vector sum is called the net force. If the net force is zero, the forces are said to be balanced, and the object remains at rest or continues to move with constant velocity. If the net force is non-zero, the forces are unbalanced, and the object accelerates in the direction of the net force. For example, when pushing a box on a surface, the applied force and the frictional force act in opposite directions. If these forces are equal in magnitude, they balance each other, and the box does not move. However, if the applied force exceeds friction, the forces become unbalanced, and the box moves. Another example is a ball floating on water, where the downward gravitational force is balanced by the upward buoyant force, resulting in no net motion. The concept of balanced forces is well illustrated by the game of tug of war. When two teams pull a rope with equal force in opposite directions, the rope remains stationary because the forces balance. If one team pulls harder, the forces become unbalanced, and the rope moves towards the stronger team. When forces act in the same direction, their magnitudes add up to produce a larger net force, causing greater acceleration. The net force's magnitude and direction depend on the magnitudes and directions of the individual forces. Calculating net force involves vector addition, which is straightforward when forces are along the same line but more complex when forces act at angles. In such cases, components of forces are resolved to find the resultant. Additionally, equal and opposite forces applied at different points on an extended object can cause rotation rather than linear motion, a concept explored in higher classes. Understanding balanced and unbalanced forces is essential for analyzing motion and forms the basis for Newton's laws of motion.

  • Multiple forces acting on an object combine to form a net force.
  • Balanced forces have equal magnitude and opposite direction, resulting in zero net force.
  • Unbalanced forces have unequal magnitudes or directions, causing acceleration.
  • Net force direction is along the larger force when forces oppose each other.
  • Forces in the same direction add to increase net force.
  • Equal and opposite forces on different points can cause rotation.
  • 📌 Balanced forces: Two or more forces whose vector sum is zero, causing no change in motion.
  • 📌 Unbalanced forces: Forces whose vector sum is non-zero, causing acceleration.
  • 📌 Net force: The vector sum of all forces acting on an object.

The Force of Friction: Often Overlooked but Always Present

Explanation

The Force of Friction: Often Overlooked but Always Present

Friction is a resistive force that acts opposite to the direction of motion or the intended motion of an object. It arises due to the roughness of surfaces in contact and the interactions at the microscopic level between the surfaces. When you try to

Practice QuestionsHow Forces Affect Motion

Includes NCERT exercise questions with answers

Q1.7. A sailor jumps out from a small boat to the shore (Fig. 6.38). As the sailor jumps forward, will the boat move? If yes, in which direction and why.

Answer:

Yes, the boat will move backward. When the sailor jumps forward, he exerts a forward force on the shore. According to Newton's third law, the shore exerts an equal and opposite force backward on the sailor. To conserve momentum, the boat moves backward as the sailor moves forward.

Explanation:

Newton's third law states that for every action, there is an equal and opposite reaction. When the sailor pushes forward to jump, the boat experiences a backward force, causing it to move backward.

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Q2.8. During a high jump event, a landing mat or sand bed is placed for the athlete to fall upon (Fig. 6.39). Explain the reason behind it.

Answer:

The landing mat or sand bed is placed to increase the time over which the athlete comes to rest, thereby reducing the impact force on the athlete's body. This cushioning prevents injuries by absorbing the energy of the fall.

Explanation:

Force experienced during impact is inversely proportional to the time over which the impact occurs (Impulse = Force × Time). Increasing the time reduces the force, making the landing safer.

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Q3.9. A hand cart loaded with vegetables collides with an identical but empty hand cart. During the collision: (i) the loaded cart exerts a force of larger magnitude on the empty cart. (ii) the empty cart exerts a force of larger magnitude on the loaded cart. (iii) neither cart exerts a force on the other. (iv) the loaded cart and the empty cart, both exert an equal magnitude of force on each other.
A.A) the loaded cart exerts a force of larger magnitude on the empty cart.
B.B) the empty cart exerts a force of larger magnitude on the loaded cart.
C.C) neither cart exerts a force on the other.
D.D) the loaded cart and the empty cart, both exert an equal magnitude of force on each other.

Answer:

the loaded cart and the empty cart, both exert an equal magnitude of force on each other. According to Newton's third law of motion, the forces two bodies exert on each other are equal in magnitude and opposite in direction, regardless of their masses or velocities.

Explanation:

Newton's third law states that forces between two interacting bodies are equal and opposite. Hence, both carts exert equal magnitude forces on each other during collision.

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Q4.10. The acceleration-mass graph for the acceleration produced by a force on objects of different masses is plotted in Fig. 6.40. Plot the force-mass graph for this case.

Answer:

From Newton's second law, Force F = mass m × acceleration a. Given the acceleration-mass graph, for each mass, acceleration is known. Multiplying mass and acceleration gives the force. Since the force is constant (as the acceleration decreases with increasing mass), the force-mass graph will be a horizontal straight line indicating constant force irrespective of mass.

Explanation:

The acceleration-mass graph shows acceleration inversely proportional to mass for constant force. Hence, force = mass × acceleration remains constant. Plotting force against mass yields a horizontal line.

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Q5.11. The velocity-time graph of an object of mass 10 kg moving along a straight line is shown in Fig. 6.41. Calculate the force acting on the object by using the graph.

Answer:

Step 1: Determine acceleration from the velocity-time graph. Acceleration a = slope of velocity-time graph = (change in velocity)/(change in time). Step 2: Use Newton's second law: F = m × a. Assuming from the graph, velocity changes from 20 m/s to 0 m/s in 4 seconds, Acceleration a = (0 - 20) / 4 = -5 m/s² (negative indicates deceleration). Mass m = 10 kg. Force F = 10 × (-5) = -50 N. The negative sign indicates force acts opposite to the direction of motion.

Explanation:

From the velocity-time graph, slope gives acceleration. Multiplying acceleration by mass gives force as per Newton's second law.

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Q6.12. A bullet of mass 50 g moving with a speed of 100 ms⁻¹ enters a heavy stationary wooden block and stops after penetrating a distance of 50 cm. Estimate the stopping force acting on the bullet (assume that the bullet undergoes constant acceleration within the block).

Answer:

Given: Mass, m = 50 g = 0.05 kg Initial velocity, u = 100 m/s Final velocity, v = 0 m/s (bullet stops) Distance, s = 50 cm = 0.5 m Step 1: Use the equation v² = u² + 2as to find acceleration a. 0 = (100)² + 2 × a × 0.5 => 0 = 10000 + a => a = -10000 / 1 = -10000 m/s² Step 2: Calculate force using F = m × a. F = 0.05 × (-10000) = -500 N The negative sign indicates the force acts opposite to the bullet's motion. Therefore, the stopping force is 500 N acting opposite to the bullet's motion.

Explanation:

Using kinematic equation to find acceleration, then Newton's second law to find force. Negative acceleration and force indicate deceleration.

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Q7.13. An ace footballer converted a penalty shot by kicking the football with a speed of 108 km h⁻¹. The estimated force they imparted was 800 N. The mass of the football was 0.4 kg. Calculate the time of contact between their foot and the ball.

Answer:

Given: Initial velocity, u = 0 m/s (ball initially at rest) Final velocity, v = 108 km/h = (108 × 1000) / 3600 = 30 m/s Force, F = 800 N Mass, m = 0.4 kg Step 1: Calculate acceleration using F = m × a => a = F / m = 800 / 0.4 = 2000 m/s² Step 2: Use equation v = u + at to find time t => t = (v - u) / a = (30 - 0) / 2000 = 0.015 s Therefore, the time of contact between the foot and the ball is 0.015 seconds.

Explanation:

Using Newton's second law to find acceleration, then using the equation of motion to find time of contact.

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Q8.14. An object of mass 2 kg moving with a constant velocity of 10 ms⁻¹ encounters a rough patch where the force of friction on the object is 7 N. At the same time, an additional constant force of 3 N opposing the motion is applied on the object. After entering the rough patch, how much distance does the object travel before coming to rest?

Answer:

Given: Mass, m = 2 kg Initial velocity, u = 10 m/s Friction force, F_friction = 7 N Additional opposing force, F_additional = 3 N Total opposing force, F_total = 7 + 3 = 10 N Step 1: Calculate acceleration using Newton's second law: F = m × a => a = F / m = -10 / 2 = -5 m/s² (negative indicates deceleration) Step 2: Use equation v² = u² + 2as to find distance s (final velocity v = 0): 0 = (10)² + 2 × (-5) × s => 0 = 100 - 10s => 10s = 100 => s = 10 m Therefore, the object travels 10 meters before coming to rest.

Explanation:

Total opposing force causes deceleration. Using equations of motion to find stopping distance.

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