How Forces Affect Motion — Class 9 Science
Exploration · Chapter 6
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6- Mathematics Part I
- Mathematics Part II
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- 16 traps corrected
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- Poetry devices
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- 12 पाठ
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- मुहावरे
Chapter summary
Key ideas & terms
- Force
- A push or pull that can change the speed, direction or shape of an object; measured in newtons (N).
- Inertia
- The natural tendency of an object to resist any change in its state of rest or uniform motion; it increases with mass.
- Momentum
- The product of an object’s mass and velocity,
; a vector pointing in the direction of motion. - Newton’s second law
- The rate of change of momentum is proportional to the applied force, leading to
. - Newton’s third law
- For every action there is an equal and opposite reaction, the two forces acting on different bodies.
- Conservation of momentum
- In the absence of an external unbalanced force, the total momentum of a system remains constant.
Extra questions & answers
List the effects a force can produce.
A force can move a body from rest, stop a moving body, increase or decrease its speed, change its direction of motion, and change its shape or size.
What is the difference between balanced and unbalanced forces?
Balanced forces are equal and opposite, so they cancel out and do not change motion; an unbalanced (net) force is left over and changes the speed or direction of the object.
State Newton’s first law of motion.
An object continues in its state of rest or of uniform motion in a straight line unless acted upon by an unbalanced external force; this is also called the law of inertia.
How is inertia related to mass?
The greater the mass of a body, the greater its inertia, so a heavier object resists changes in its state of motion more strongly than a lighter one.
Define momentum and give its SI unit.
Momentum is the product of mass and velocity,
State Newton’s second law and the formula it gives.
The rate of change of momentum of a body is directly proportional to the applied force and in the same direction, which gives
Why does the same force give a smaller acceleration to a heavier body?
Because
State Newton’s third law with an example.
To every action there is an equal and opposite reaction; for example, when a canoeist pushes water backwards with the paddle, the water pushes the canoe forward.
Why does a gun recoil when fired?
By conservation of momentum, the forward momentum given to the bullet is balanced by an equal and opposite backward momentum given to the gun, which is felt as recoil.
State the law of conservation of momentum.
When no external unbalanced force acts on a system, its total momentum before an interaction equals its total momentum after, as in collisions and recoil.
Think It Over
Why does a canoe move forward when the canoeist pushes water backwards with their paddle and why does it move faster when they push harder?
When the canoeist pushes water backwards, the paddle exerts a force on the water backwards. By Newton's third law the water exerts an equal and opposite force on the paddle and canoe forwards, so the canoe moves forward. When the canoeist pushes harder the force on the water is larger, so the reaction force on the canoe is also larger, giving a larger net forward force and thus larger acceleration and increase in velocity, so the canoe moves faster.
Suppose the same canoeist uses the same paddle force in two different canoes, one empty and one carrying another passenger. In which case will the canoe move faster?
For the same net force
Pause and Ponder
1. A weightlifter lifts a barbell (Fig. 6.8). List two forces that are acting on the barbell. Are these forces balanced if the weightlifter keeps the barbell steady?
Two forces on the barbell are (i) the gravitational force (weight)
2. Two players R and S are participating in an arm-wrestling match (Fig. 6.9). At the instant, when the arms tilt to the front direction (out of the page towards you), are the forces exerted by the players balanced? If not, which player exerted the larger force?
No, the forces are not balanced at that instant because there is motion with acceleration in the forward direction. A net force must be acting in the direction of motion. Since the arms tilt forward (towards you), the player who is causing that motion exerts the larger force. If R is on that side pushing forward, R exerts the larger force; the net force is in R's direction. In general the winner whose side the arms move toward exerts the larger force.
Pause and Ponder
3. An object is moving with a constant velocity. Is there a net force acting upon it?
No. By Newton's first law, if velocity is constant (both magnitude and direction unchanged) the acceleration is zero, so the net force
4. Suppose, no net force is acting on an object. Which of the following situations are possible? (i) Object remains at rest if at rest.
Possible. This is directly stated by Newton's first law. If
4. Suppose, no net force is acting on an object. Which of the following situations are possible? (ii) Object keeps moving with a constant velocity if already moving.
Possible. If
4. Suppose, no net force is acting on an object. Which of the following situations are possible? (iii) Object is moving with a constant acceleration.
Not possible. Constant acceleration means velocity is changing, which requires a non-zero net force by
5. In the real world, it is difficult to find a situation where no forces are acting on an object. But by applying additional forces, a condition can be achieved where the net force on the object is zero. Explain with the help of an example.
A zero net force can occur when several forces balance each other. For example, a box being pushed on a floor at constant velocity: the forward push
Pause and Ponder
6. A toy car of mass 100 g is moving with a constant velocity of 0.5 m s–1. What is the net force acting on the toy car?
Constant velocity means acceleration
7. Two children of different masses are sitting on identical swings. To impart identical initial acceleration, for which child would you require to apply a larger force? Explain why.
From Newton's second law
8. How are glass items packed for transportation using a bubble wrap or hay protected from damage?
Bubble wrap or hay increases the time
Pause and Ponder
9. Why does a fireperson sometimes struggle when holding the pipe issuing water?
Water is expelled forward at high speed by the pump. By Newton's third law the water exerts an equal and opposite backward force on the pipe and on the person holding it. This reaction or recoil force pushes the person backwards, so a strong grip and bracing are needed to balance it. The larger the flow rate and speed, the larger the recoil force.
10. Suppose a spacecraft is moving in a region of space where the gravitational force acting upon it is negligible. Suggest how can it change its velocity.
In the absence of external forces the spacecraft moves with constant velocity (Newton's first law). To change velocity it must produce a net force by expelling mass, as a rocket does. Firing its thrusters expels gas in one direction; the gas exerts an opposite reaction force on the spacecraft (Newton's third law), accelerating it in the opposite direction to the exhaust. By firing forward, backward or sideways the craft can accelerate, decelerate or change direction, according to
Revise, Reflect, Refine
1. Using a horizontal force F, a table is moved across the floor at a constant velocity. How much is the frictional force exerted by the floor on the table?
Constant velocity means acceleration zero, so net horizontal force is zero. Therefore friction exactly balances the applied force. The magnitude of friction is
2. For a ball moving on a smooth frictionless surface, choose the appropriate option that will make the following statements physically correct. (i) If no net force is applied on the ball, the velocity of the ball will remain the same/increase/decrease.
remain the same. With zero net force on a frictionless (no friction) surface, by Newton's first law the ball continues with its existing velocity; magnitude and direction do not change.
2. For a ball moving on a smooth frictionless surface, choose the appropriate option that will make the following statements physically correct. (ii) If a net force is applied on the ball in the direction of its motion, the magnitude of the velocity of the ball will remain the same/increase/decrease.
increase. A net force in the direction of motion produces acceleration in that direction (
2. For a ball moving on a smooth frictionless surface, choose the appropriate option that will make the following statements physically correct. (iii) If a net force is applied on the ball in a direction opposite to the direction of its motion, the magnitude of the velocity of the ball will remain the same/increase/decrease.
decrease. A net force opposite to motion produces acceleration opposite to velocity, so the ball slows down and magnitude of velocity decreases (eventually it may stop and reverse).
3. Two blocks P and Q on a smooth horizontal surface are shown in Fig. 6.36a and Fig. 6.36b. Two forces of magnitudes 4 N and 5 N are acting in opposite directions on block P, while block Q is moving with a constant velocity. Which of the following statement is correct? (i) P experiences a net force and Q does not experience a net force. (ii) P does not experience a net force and Q experiences a net force. (iii) Both P and Q experience a net force. (iv) Neither P nor Q experiences a net force.
Correct option is (i). For block P the opposite forces are unequal: net force
4. While practising for the snake boat race (Vallum kalli in Kerala), 100 oarsmen are rowing a boat together. Out of these, 95 row backwards to propel the boat forward. But by mistake, 5 oarsmen row in the opposite direction. If each oarsman applies a horizontal force of 200 N, what is the net force on the snake boat? (Ignore drag forces, air friction, etc.)
Take forward as positive. Force by 95 oarsmen forward:
5. When a net force acts on an object, we observe that the object accelerates: (i) opposite to the direction of force, with acceleration proportional to the force acting on the object. (ii) opposite to the direction of force, with acceleration proportional to the mass of the object. (iii) in the direction of force, with acceleration inversely proportional to the force acting on the object. (iv) in the direction of force, with acceleration proportional to the force acting on the object.
Correct is (iv). By Newton's second law
6. The position-time graph for four objects A, B, C and D moving along a straight line are given in Fig. 6.37. A net force acts on: (i) Object A (ii) Object B (iii) Object C (iv) Object D
A net force acts only when velocity is not constant, i.e. when the position–time graph is curved rather than a straight line. From Fig. 6.37: Object A is an inclined straight line (constant velocity, zero net force); Object B is a horizontal line (at rest, zero net force); Object C is a curved line (velocity changing, so a non-zero net force acts); Object D is a straight declining line (constant velocity, zero net force). Hence a net force acts only on Object C — option (iii).
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.
Yes, the boat moves. As the sailor jumps forward, they push backward on the boat with their feet; by Newton's third law the boat pushes the sailor forward, letting them reach the shore. The equal and opposite reaction on the boat is directed backward, so the boat moves backward, away from the shore.
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.
The mat increases the time interval
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.
Correct is (iv). By Newton's third law the forces of interaction between the two carts are equal in magnitude and opposite in direction, regardless of their masses or loading. They act on different objects, so they do not cancel.
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.
For a fixed force
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,.
From Fig. 6.41 the velocity rises linearly from
12. A bullet of mass 50 g moving with a speed of 100 m s–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).
Given
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.
Final speed
14. An object of mass 2 kg moving with a constant velocity of 10 m s–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?
Initial velocity
15. A tractor pulls a harrow (a ploughing tool) of mass m1 with a net force F resulting in an acceleration of a1. The same tractor pulls a trolley of mass m2 with a force F producing an acceleration of a2. If the tractor now pulls the trolley with the harrow placed on it (with the same force F), then obtain an expression for the resulting acceleration in terms of a1 and a2. Ignore friction.
From
16. When the pole of a bar magnet is brought close to a magnetic compass, the bar magnet and the compass needle (which is also a magnet) exert a magnetic force on each other. As per Newton’s third law of motion, both the forces are equal in magnitude and opposite in direction. However, the compass needle moves, whereas the bar magnet does not move (Fig. 6.42). Explain why.
The action-reaction forces are equal, but acceleration