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Q5.23(b):
Explain why (b) passengers are thrown forward from their seats when a speeding bus stops suddenly,
Solution :
Step 1: Identifying the Principle of Inertia
The motion of passengers in a bus is governed by Newton’s First Law of Motion, also known as the Law of Inertia. This law states that every object continues in its state of rest or of uniform motion in a straight line unless compelled to change that state by an external impressed force [Per Newton’s First Law].
Step 2: Analysis of Initial State
Consider a bus moving with a constant velocity $v$. As the passengers sit inside the bus, their entire bodies—including the lower part in contact with the seat and the upper torso—are also moving with the same velocity $v$ relative to the ground.
Step 3: Effect of Sudden Deceleration
When the brakes are applied suddenly, the bus experiences a rapid deceleration.
- The lower body: Because the lower part of the passenger’s body is in contact with the bus seat, the frictional force between the seat and the passenger, combined with the seat belt or physical bracing, causes this part to decelerate along with the bus.
- The upper body: The upper part of the body is not directly subjected to the braking force applied to the chassis. According to the Law of Inertia of Motion, this part of the body tends to maintain its state of uniform motion at velocity $v$.
Step 4: Theoretical Representation of Displacement
Since the lower body slows down while the upper body continues at $v$, the passenger undergoes a relative displacement forward. Mathematically, if the bus comes to rest at time $t$, the upper body effectively continues forward due to its inertia until an external force (such as a seat belt or the back of the front seat) provides an impulse $J = \int F dt$ to change its momentum.
Step 5: Conclusion via Momentum Analysis
The inertia of the passenger's mass $m$ manifests as a tendency to preserve the initial momentum $p = mv$. When the bus stops, the seat exerts a force to stop the lower body, but the inertia of the upper body causes it to continue moving forward relative to the decelerating vehicle [By Principle of Conservation of Momentum/Inertia].
Final Solution: Passengers are thrown forward because of the Law of Inertia of Motion, which dictates that the upper body of the passenger tends to maintain its state of uniform motion even when the bus (and the lower body in contact with the seat) decelerates suddenly.
More Questions from Class 11 Physics Laws of Motion EXERCISES
- Q4.1(a): Give the magnitude and direction of the net force acting on a drop of rain falling down with a constant speed,
- Q4.1(b): Give the magnitude and direction of the net force acting on a cork of mass 10 g floating on water,
- Q4.1(c): Give the magnitude and direction of the net force acting on a kite skillfully held stationary in the sky,
- Q4.1(d): Give the magnitude and direction of the net force acting on a car moving with a constant velocity of 30 km/h on a rough road,
- Q4.1(e): Give the magnitude and direction of the net force acting on a high-speed electron in space far from all material objects, and free of electric and magnetic fields.
- Q4.10: A body of mass 0.40 kg moving initially with a constant speed of 10 (m s^{-1}) to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be (t = 0), the position of the body at that time to be (x = 0), and predict its position at (t = -5) s, 25 s, 100 s.
- Q4.11(a): A truck starts from rest and accelerates uniformly at 2.0 (m s^{-2}). At (t = 10) s, a stone is dropped by a person standing on the top of the truck (6 m high from the ground). What are the velocity of the stone at (t = 11)s ? (Neglect air resistance.)
- Q4.11(b): A truck starts from rest and accelerates uniformly at 2.0 (m s^{-2}). At (t = 10) s, a stone is dropped by a person standing on the top of the truck (6 m high from the ground). What are the acceleration of the stone at (t = 11)s ? (Neglect air resistance.)
- Q4.12(a): A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 (m s^{-1}). What is the trajectory of the bob if the string is cut when the bob is at one of its extreme positions,
- Q4.12(b): A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 (m s^{-1}). What is the trajectory of the bob if the string is cut when the bob is at its mean position.
- Q4.13(a): A man of mass 70 kg stands on a weighing scale in a lift which is moving upwards with a uniform speed of 10 (m s^{-1}). What would be the readings on the scale in this case?
- Q4.13(b): A man of mass 70 kg stands on a weighing scale in a lift which is moving downwards with a uniform acceleration of 5 (m s^{-2}). What would be the readings on the scale in this case?
- Q4.13(c): A man of mass 70 kg stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of 5 (m s^{-2}). What would be the readings on the scale in this case?
- Q4.13(d): A man of mass 70 kg stands on a weighing scale in a lift. What would be the reading if the lift mechanism failed and it hurtled down freely under gravity ?
- Q4.14(a): Figure 4.16 shows the position-time graph of a particle of mass 4 kg. What is the force on the particle for (t < 0), (t > 4) s, (0 < t < 4) s? (Consider one-dimensional motion only).
- Q4.14(b): Figure 4.16 shows the position-time graph of a particle of mass 4 kg. What is the impulse at (t = 0) and (t = 4) s ? (Consider one-dimensional motion only).
- Q4.15(i): Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force (F = 600) N is applied to the 10 kg body (A) along the direction of string. What is the tension in the string?
- Q4.15(ii): Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force (F = 600) N is applied to the 20 kg body (B) along the direction of string. What is the tension in the string?
- Q4.16: Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.
- Q4.17: A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.
- Q4.18: Two billiard balls each of mass 0.05 kg moving in opposite directions with speed 6 (m s^{-1}) collide and rebound with the same speed. What is the impulse imparted to each ball due to the other ?
- Q4.19: A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 (m s^{-1}), what is the recoil speed of the gun ?
- Q4.2(a): A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble, during its upward motion,
- Q4.2(b): A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble, during its downward motion,
- Q4.2(c): A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble, at the highest point where it is momentarily at rest. Do your answers change if the pebble was thrown at an angle of 45(^{\circ}) with the horizontal direction? Ignore air resistance.
- Q4.20: A batsman deflects a ball by an angle of 45(^{\circ}) without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball ? (Mass of the ball is 0.15 kg.)
- Q4.21: A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N ?
- Q4.22: If the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks :
- Q4.23(a): Explain why a horse cannot pull a cart and run in empty space,
- Q4.23(b): Explain why passengers are thrown forward from their seats when a speeding bus stops suddenly,
- Q4.23(c): Explain why it is easier to pull a lawn mower than to push it,
- Q4.23(d): Explain why a cricketer moves his hands backwards while holding a catch.
- Q4.3(a): Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, just after it is dropped from the window of a stationary train,
- Q4.3(b): Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, just after it is dropped from the window of a train running at a constant velocity of 36 km/h,
- Q4.3(c): Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, just after it is dropped from the window of a train accelerating with 1 (m s^{-2}),
- Q4.3(d): Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, lying on the floor of a train which is accelerating with 1 (m s^{-2}), the stone being at rest relative to the train. Neglect air resistance throughout.
- Q4.4: One end of a string of length (l) is connected to a particle of mass (m) and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed (v) the net force on the particle (directed towards the centre) is : (T) is the tension in the string.
- Q4.5: A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of 15 (m s^{-1}). How long does the body take to stop ?
- Q4.6: A constant force acting on a body of mass 3.0 kg changes its speed from 2.0 (m s^{-1}) to 3.5 (m s^{-1}) in 25 s. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force ?
- Q4.7: A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. Give the magnitude and direction of the acceleration of the body.
- Q4.8: The driver of a three-wheeler moving with a speed of 36 km/h sees a child standing in the middle of the road and brings his vehicle to rest in 4.0 s just in time to save the child. What is the average retarding force on the vehicle ? The mass of the three-wheeler is 400 kg and the mass of the driver is 65 kg.
- Q4.9: A rocket with a lift-off mass 20,000 kg is blasted upwards with an initial acceleration of 5.0 (m s^{-2}). Calculate the initial thrust (force) of the blast.
- Q5.1(a): Give the magnitude and direction of the net force acting on (a) a drop of rain falling down with a constant speed,
- Q5.1(b): Give the magnitude and direction of the net force acting on (b) a cork of mass 10 g floating on water,
- Q5.1(c): Give the magnitude and direction of the net force acting on (c) a kite skillfully held stationary in the sky,
- Q5.1(d): Give the magnitude and direction of the net force acting on (d) a car moving with a constant velocity of 30 km/h on a rough road,
- Q5.1(e): Give the magnitude and direction of the net force acting on (e) a high-speed electron in space far from all material objects, and free of electric and magnetic fields.
- Q5.10: A body of mass 0.40 kg moving initially with a constant speed of $10 m s^{-1}$ to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be $t = 0$, the position of the body at that time to be $x = 0$, and predict its position at $t = –5 s$, $25 s$, $100 s$.
- Q5.11(a): A truck starts from rest and accelerates uniformly at $2.0 m s^{-2}$. At $t = 10 s$, a stone is dropped by a person standing on the top of the truck (6 m high from the ground). What are the (a) velocity of the stone at $t = 11s$ ? (Neglect air resistance.)
- Q5.11(b): A truck starts from rest and accelerates uniformly at $2.0 m s^{-2}$. At $t = 10 s$, a stone is dropped by a person standing on the top of the truck (6 m high from the ground). What are the (b) acceleration of the stone at $t = 11s$ ? (Neglect air resistance.)
- Q5.12(a): A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is $1 m s^{-1}$. What is the trajectory of the bob if the string is cut when the bob is (a) at one of its extreme positions,
- Q5.12(b): A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is $1 m s^{-1}$. What is the trajectory of the bob if the string is cut when the bob is (b) at its mean position.
- Q5.13(a): A man of mass 70 kg stands on a weighing scale in a lift which is moving (a) upwards with a uniform speed of $10 m s^{-1}$,
- Q5.13(b): A man of mass 70 kg stands on a weighing scale in a lift which is moving (b) downwards with a uniform acceleration of $5 m s^{-2}$,
- Q5.13(c): A man of mass 70 kg stands on a weighing scale in a lift which is moving (c) upwards with a uniform acceleration of $5 m s^{-2}$. What would be the readings on the scale in each case?
- Q5.13(d): A man of mass 70 kg stands on a weighing scale in a lift which is moving (d) What would be the reading if the lift mechanism failed and it hurtled down freely under gravity ?
- Q5.14(a): Figure 5.16 shows the position-time graph of a particle of mass 4 kg. What is the (a) force on the particle for $t < 0$, $t > 4 s$, $0 < t < 4 s$?
- Q5.14(b): Figure 5.16 shows the position-time graph of a particle of mass 4 kg. What is the (b) impulse at $t = 0$ and $t = 4 s$ ? (Consider one-dimensional motion only).
- Q5.15(i): Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force $F = 600 N$ is applied to (i) A, along the direction of string. What is the tension in the string in each case?
- Q5.15(ii): Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force $F = 600 N$ is applied to (ii) B along the direction of string. What is the tension in the string in each case?
- Q5.16: Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.
- Q5.17: A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.
- Q5.18: Two billiard balls each of mass 0.05 kg moving in opposite directions with speed $6 m s^{-1}$ collide and rebound with the same speed. What is the impulse imparted to each ball due to the other ?
- Q5.19: A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is $80 m s^{-1}$, what is the recoil speed of the gun ?
- Q5.2(a): A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble, (a) during its upward motion,
- Q5.2(b): A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble, (b) during its downward motion,
- Q5.2(c): A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble, (c) at the highest point where it is momentarily at rest. Do your answers change if the pebble was thrown at an angle of 45° with the horizontal direction? Ignore air resistance.
- Q5.20: A batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball ? (Mass of the ball is 0.15 kg.)
- Q5.21: A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N ?
- Q5.22: If, A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N, the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks :
- Q5.23(a): Explain why (a) a horse cannot pull a cart and run in empty space,
- Q5.23(c): Explain why (c) it is easier to pull a lawn mower than to push it,
- Q5.23(d): Explain why (d) a cricketer moves his hands backwards while holding a catch.
- Q5.3(a): Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, (a) just after it is dropped from the window of a stationary train,
- Q5.3(b): Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, (b) just after it is dropped from the window of a train running at a constant velocity of 36 km/h,
- Q5.3(c): Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, (c) just after it is dropped from the window of a train accelerating with $1 m s^{-2}$,
- Q5.3(d): Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, (d) lying on the floor of a train which is accelerating with $1 m s^{-2}$, the stone being at rest relative to the train. Neglect air resistance throughout.
- Q5.4: One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is : $T$ is the tension in the string. [Choose the correct alternative].
- Q5.5: A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of $15 m s^{-1}$. How long does the body take to stop ?
- Q5.6: A constant force acting on a body of mass 3.0 kg changes its speed from $2.0 m s^{-1}$ to $3.5 m s^{-1}$ in 25 s. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force ?
- Q5.7: A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. Give the magnitude and direction of the acceleration of the body.
- Q5.8: The driver of a three-wheeler moving with a speed of 36 km/h sees a child standing in the middle of the road and brings his vehicle to rest in 4.0 s just in time to save the child. What is the average retarding force on the vehicle ? The mass of the three-wheeler is 400 kg and the mass of the driver is 65 kg.
- Q5.9: A rocket with a lift-off mass 20,000 kg is blasted upwards with an initial acceleration of $5.0 m s^{-2}$. Calculate the initial thrust (force) of the blast.
CBSE Solutions for Class 11 Physics Laws of Motion
Chapters in CBSE - Class 11 Physics
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