1. Using a horizontal force , a table is moved across the floor at a constant velocity. How much is the frictional force exerted by the floor on the table?
Step 1: Understand the Question
The table is moving with constant velocity.
According to Newton’s First Law of Motion, if an object moves with constant velocity, its acceleration is zero.
Therefore, the net force acting on the object is zero.
Step 2: Identify the Forces Acting on the Table
The horizontal forces acting on the table are:
- Applied force (F) acting in the forward direction.
- Frictional force (f) exerted by the floor, acting in the opposite direction.
Step 3: Apply Newton’s First Law
Since the table moves with constant velocity,
Therefore,
Step 4: Calculate the Frictional Force
Rearranging the equation,
f = F
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.
(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.
(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.
(i) If no net force is applied on the ball, the velocity of the ball will ________.
Explanation
No net force means no acceleration.
Therefore, the ball continues to move with the same velocity.
Answer : Remain the same
(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 ________.
Explanation
The applied force acts in the same direction as the motion.
This produces positive acceleration.
As a result, the speed (magnitude of velocity) of the ball increases.
Answer: Increases
(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 ________.
Explanation
- The applied force acts opposite to the direction of motion.
- This produces retardation (negative acceleration).
- Therefore, the speed of the ball decreases.
Answer: Decreases
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?
1. P experiences a net force and Q does not experience a net force.
2. P does not experience a net force and Q experiences a net force.
3. Both P and Q experience a net force.
4. Neither P nor Q experiences a net force.
Step 1: Understand the Situation for Block P
Two horizontal forces act on block P:
One force = 5 N
Other force = 4 N
Both act in opposite directions.
Since the forces are opposite, the net force is the difference between them.
Net Force = 5 N – 4 N
Net Force = 1 N
Therefore, block P experiences a net force of 1 N in the direction of the 5 N force.
Step 2: Understand the Situation for Block Q
Block Q is moving with constant velocity.
According to Newton’s First Law of Motion, an object moving with constant velocity has zero acceleration.
From Newton’s Second Law,
F = ma
Since
a = 0,
F = m × 0 = 0
Therefore, the net force acting on block Q is zero.
Step 3: Check Each Option
Option 1: P experiences a net force and Q does not experience a net force.
P has a net force of 1 N. ✔
Q has no net force. ✔
This statement is correct.
Option 2: P does not experience a net force and Q experiences a net force.
Incorrect.
Option 3: Both P and Q experience a net force.
Incorrect because Q has no net force.
Option 4: Neither P nor Q experiences a net force.
Incorrect because P experiences a net force of 1 N.
Final Correct Answer: P experiences a net force and Q does not experience a 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.)
Step 1: Write the Given Data
Total number of oarsmen = 100
Number of oarsmen rowing in the correct direction = 95
Number of oarsmen rowing in the opposite direction = 5
Force applied by each oarsman = 200 N
Step 2: Calculate the Total Forward Force
The forward force is produced by the 95 oarsmen rowing in the correct direction.
Forward Force = 95 × 200
= 19000 N
Step 3: Calculate the Opposing Force
The 5 oarsmen rowing in the opposite direction produce a force opposite to the boat’s motion.
Opposing Force = 5 × 200
= 1000 N
Step 4: Calculate the Net Force
Since the two forces act in opposite directions,
Net Force = Forward Force – Opposing Force
= 19000-1000
= 18000 N
Final Answer:
Net Force = 18,000 N
The net force of 18,000 N acts in the forward direction, i.e., in the direction of the 95 oarsmen.
Explanation
The forces applied by the two groups of oarsmen are opposite to each other.
The larger forward force overcomes the smaller opposing force.
Therefore, the boat experiences an unbalanced net force of 18,000 N, causing it to move forward.
Answer:
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.
Step 1: Recall Newton’s Second Law of Motion
Newton’s Second Law states that:
The acceleration produced in an object is directly proportional to the net force acting on it and occurs in the direction of the applied force.
Mathematically,
F = ma
or
a = F/ m
where,
= Mass of the object
= Acceleration produced
Step 2: Analyse Each Option
(i) Opposite to the direction of force, with acceleration proportional to the force acting on the object.
Incorrect
Acceleration always occurs in the direction of the net force, not opposite to it.
(ii) Opposite to the direction of force, with acceleration proportional to the mass of the object.
Incorrect
Acceleration is not proportional to mass. In fact,
a ∝ 1 / m
Also, acceleration is not opposite to the force.
(iii) In the direction of force, with acceleration inversely proportional to the force acting on the object.
Incorrect, Acceleration is in the direction of force, but it is directly proportional to force, not inversely proportional.
(iv) In the direction of force, with acceleration proportional to the force acting on the object.
Correct, According to Newton’s Second Law:
a ∝ F
and acceleration is produced in the direction of the applied force.
Final Answer:
(iv) In the direction of force, with acceleration proportional to the force acting on the object.
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
Step 1: Recall the Concept
According to Newton’s Second Law of Motion,
F = ma
where:
F = Net force
m = Mass of the object
a = Acceleration
A net force acts only when the object is accelerating (i.e., when its velocity changes).
Step 2: Analyse the Position–Time Graphs
Object A
The graph is a straight line.
A straight line on a position–time graph indicates constant velocity.
Therefore, acceleration is zero.
F = ma = m × 0 = 0
No net force acts on Object A.
Object B
The graph is curved, with the slope increasing with time.
Increasing slope means the velocity is increasing.
Hence, the object is accelerating.
Since acceleration is not zero,
F = ma ≠ 0
A net force acts on Object B.
Object C
The graph is also a straight line.
Straight-line graph indicates constant velocity.
Therefore, acceleration is zero.
F = 0
No net force acts on Object C.
Object D
The graph is horizontal, indicating that the position remains constant.
Therefore, the object is at rest.
Velocity and acceleration are both zero.
F = 0
No net force acts on Object D.
Step 3: Choose the Correct Option
Only Object B is accelerating.
Therefore, a net force acts only on Object B.
Final Answer
Correct Option: (ii) Object B
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.
Step 1: Understand the Situation
Initially, both the sailor and the boat are at rest.
When the sailor jumps towards the shore, he pushes the boat backward with his feet.
Step 2: Apply Newton’s Third Law of Motion
According to Newton’s Third Law of Motion:
For every action, there is an equal and opposite reaction.
Action: The sailor pushes the boat backward.
Reaction: The boat pushes the sailor forward with an equal and opposite force.
Step 3: Motion of the Boat
Since the sailor exerts a backward force on the boat, the boat experiences an equal force in the opposite direction and moves backward, i.e., away from the shore.
Step 4: Reason
The boat is free to move on water because there is very little friction between the boat and the water. Therefore, even a small backward force causes the boat to move in the opposite direction.
Final Answer
Yes, the boat will move. It moves backward (away from the shore) because when the sailor jumps forward, he pushes the boat backward. According to Newton’s Third Law of Motion, the boat experiences an equal and opposite force and moves in the opposite direction.
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.
Step 1: Understand the Situation
When a high jumper lands after crossing the bar, their body is moving with a certain velocity. On landing, the athlete’s body must come to rest.
According to Newton’s Second Law of Motion,
F = Δp / Δt
where:
Δp = Change in momentum
Δt = Time taken to stop
Step 2: Apply the Concept of Momentum
When the athlete lands:
The change in momentum (Δp) is the same whether they land on hard ground or on a soft mat.
However, the time taken to stop (Δt) is different.
A landing mat or sand bed increases the time over which the athlete comes to rest.
Step 3: Effect on the Force
Since the stopping time increases,
F = Δp/Δt
As Δt increases, the force F decreases.
Therefore, the impact force on the athlete’s body is much smaller.
Step 4: Conclusion
The reduced impact force lowers the chances of injuries and provides a safer landing for the athlete.
Final Answer:
A landing mat or sand bed is placed so that the athlete takes a longer time to come to rest after landing. According to Newton’s Second Law of Motion (F = Δp/ Δt), increasing the stopping time decreases the impact force. Hence, the landing mat or sand bed reduces the force of impact and protects the athlete from injuries.
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.
Step 1: Understand the Situation
Two hand carts collide:
One cart is loaded with vegetables.
The other cart is empty.
Both carts exert forces on each other during the collision.
Step 2: Apply Newton’s Third Law of Motion
According to Newton’s Third Law of Motion:
For every action, there is an equal and opposite reaction.
This means that whenever one object exerts a force on another object, the second object exerts an equal force in the opposite direction on the first object.
Step 3: Analyse the Options
Option (i) The loaded cart exerts a force of larger magnitude on the empty cart.
Answer: Incorrect.
According to Newton’s Third Law, the force cannot be larger.
Option (ii) The empty cart exerts a force of larger magnitude on the loaded cart.
Answer: Incorrect.
The forces are equal in magnitude.
Option (iii) Neither cart exerts a force on the other.
Answer: Incorrect.
During a collision, both carts definitely exert forces on each other.
Option (iv) The loaded cart and the empty cart both exert an equal magnitude of force on each other.
Answer: Correct.
The forces are equal in magnitude but opposite in direction.
Final Answer ✔ Correct Option: (iv)
The loaded cart and the empty cart both exert equal magnitude forces on each other during the collision.
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.
Step 1: Recall Newton’s Second Law of Motion
According to Newton’s Second Law of Motion,
F = ma
where:
Step 2: Analyse the Given Graph
The given graph shows that as the mass of the object increases, its acceleration decreases.
This means:
a × 1/m
The applied force is the same for all the objects.
Step 3: Determine the Force
Using the equation,
F = ma
As the mass increases, the acceleration decreases by the same proportion. Therefore, the product m × a remains constant.
Hence, the force acting on each object is constant.
Final Answer
The force–mass graph is a horizontal straight line because the same force acts on all the objects, irrespective of their masses. Although the acceleration decreases with increasing mass, the product of mass and acceleration remains constant according to Newton’s Second Law (F = ma)
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.
Step 1: Write the Given Data
Mass of the object, m = 10kg
Velocity–time graph is given.
From the graph:
Initial velocity, u = 0 ms-1
Final velocity, v = 20ms-1
Time taken, t = 10s
(Read these values from the graph.)
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).
Step 4: Interpret the Result
The negative sign indicates that the force acts opposite to the direction of motion of the bullet.
Therefore, the magnitude of the stopping force is: ∣F∣=500 N
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.
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?
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.
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.
According to Newton’s Third Law of Motion, whenever two objects interact, they exert equal and opposite forces on each other. Therefore, the bar magnet and the compass needle apply equal magnetic forces on one another.
However, the effect of these forces is different because:
- The compass needle is very light and is mounted on a pivot, allowing it to rotate freely.
- The bar magnet is much heavier and is usually held firmly in the hand or placed on a surface, so it cannot move easily.
According to Newton’s Second Law of Motion,
a = F/ m
For the same force:
- The compass needle, having less mass, undergoes a larger acceleration and moves easily.
- The bar magnet, having greater mass and being supported, undergoes very little acceleration, so its motion is not noticeable.
Hence, both magnets exert equal and opposite forces, but only the compass needle shows visible motion because it is lighter and free to rotate.
Answer: The compass needle moves because it is light and free to rotate, whereas the bar magnet is heavier and usually held firmly or placed on a surface. Although both experience equal and opposite magnetic forces, the compass needle undergoes greater acceleration and moves, while the bar magnet does not show noticeable motion.