DYNAMICS CHAPTER # 03 PHYSICS 9TH – Short / Detailed Question Answers

 PHYSICS 9TH – Short / Detailed Question Answers

DYNAMICS
CHAPTER # 03

Q.1: Describe force and its unit.
Ans: Force:
Force is the agent that changes the state of rest or uniform motion of a body. Its S.I unit is Newton (N). One Newton (1N) is the amount of force that can produce $1 \, \text{ms}^{-2}$ acceleration in $1 \, \text{kg}$ mass. An object at rest needs a force to get moving; a moving object needs a force to come to rest or change its direction. The magnitude of a force can be measured using a spring balance.

In short, force is required to change the position, state, or shape of an object. It can act as a pull or push agent. Force produces acceleration and can produce distortion. It is a vector quantity.

Q.2: What is momentum?
Ans: Momentum:
If a cricket ball and a car are moving at the same speed, we cannot stop the car with hands but we can stop the ball.

On the other hand, it is not possible for a person to stop even a slow-moving truck by pulling from the backside. The momentum depends upon the quantity of mass and velocity of the object. The greater the mass, the greater will be the momentum. Similarly, the faster the speed, the greater will be momentum.

Definition:

Momentum is defined as the quantity of motion contained in a body. Momentum is the product of the mass and velocity of a moving object. In terms of an equation, the momentum of an object is equal to the mass multiplied by the velocity of the object.

$$\text{Momentum} = \text{mass} \times \text{velocity}$$

Symbolically, the momentum is represented by $p$. Thus, the above equation can be written as:

$$p = mv$$

where $m$ is the mass and $v$ is the velocity. The momentum is a vector quantity.

S.I Unit of Momentum:

A mass unit is multiplied by a velocity unit to provide a momentum unit. This is consistent with the equation for momentum. The S.I unit of momentum is described below:

$$\text{Momentum} = \text{mass} \times \text{velocity}$$ $$= \text{kg} \times \text{ms}^{-1} = \text{kgms}^{-1} = \text{kgms}^{-2} \times \text{s}$$

or $Ns$ (Newton second).

Q.3: Describe momentum in terms of force. OR Derive the equation of momentum in terms of force.
Ans: Momentum in terms of force:

We can also say that the change in momentum is equal to the force multiplied by the time interval for which it was applied. Consider a body of mass $m$, moving with initial velocity $v_i$. A force $F$ acts on the body to produce acceleration $a$, therefore the final velocity after time $t$ will become $v_f$. Note that if $p = mv$ and $m$ is constant, and then the change in velocity changes the momentum of the body.

$$p_i = mv_i$$ $$p_f = mv_f$$

and

$$p_f - p_i = mv_f - mv_i \, (\text{change in momentum})$$ $$p_f - p_i = m(v_f - v_i)$$

Dividing both sides by $t$:

Since the rate of change of velocity is acceleration:

According to Newton’s second law of motion, $F = ma$

Therefore:

So,

Q.4: Write a note on safety devices.

Ans: Safety Devices:

The equation $\Delta p = Ft$ is important when it comes to considering a number of safety features in our lives. If we are moving, we have momentum. To stop moving, a force must be applied. According to the equation $p = Ft$, if we take a longer time to stop, a smaller force will be used to slow us down.

Observe a car to identify the safety measures taken to reduce the risk of injuries in case of a road accident. The car bumpers and grills are designed to provide extra time to reduce speed before any collision.

We can find some crumple zones or bumpers on the front and backside. Seat belts are provided to hold the passengers from moving suddenly. There are extra cushions and airbags as well. These measures provide extra time to change the momentum of the passenger inside it. This means that the force acting on the passenger is less to prevent the risk of fatal injuries.

Styrofoam packing reduces the effect of sudden shock. Helmets protect from a direct strike on the head and provide extra time to reduce speed before something strikes it. Different safety helmets are used by workers, riders, and sportsmen.

Q.5: Explain the law of conservation of momentum.

Ans: Law of Conservation of Momentum:

The concept of momentum is important particularly in situations when two or more bodies are interacting with each other. It is a very useful quantity when it comes to calculating what happens in a collision or explosion. It always conserves when the colliding bodies are in an isolated system. This means that when bodies collide, no external forces act on the bodies.

Thus, the Law of Conservation of Momentum states that:

“The total momentum of an isolated system always remains constant.”

For simplicity, we consider a system of two billiard balls of mass $m_1$ and $m_2$ moving in a straight line with velocities $u_1$ and $u_2$, respectively, where $u_1$ is greater than $u_2$.

Total momentum of the system before collision:

$$m_1 u_1 + m_2 u_2$$

According to the Law of Conservation of Momentum:

$$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$$

Q.6: State and explain Newton’s first law of motion.

Ans: First Law of Motion:

We have often observed the table placed in our classroom. It always remains at the same place until we apply some force to move it. Like a book placed on the table remains at its place unless someone picks it back. Similarly, a satellite in space continuously moves with constant speed because there is no air or force of friction in space.

Contrary to the above examples, a ball rolling on the ground, however, stops after some time because the friction of the ground and air resistance exert force on it and change its state of motion or direction of motion. We can define Newton’s first law of motion as:

“A body continues its state of rest or uniform motion in a straight line unless an external force acts on it.”

Q.7: Define inertia. Which law of motion is also called the law of inertia?

Ans: Inertia:

Newton’s first law is also called the Law of Inertia. We have observed that when we put our bag on the seat next to us and the bus stops suddenly, the bag slides forward off the seat.

The bag was initially moving forward because it was on a moving bus. When the bus stopped, the bag continued moving forward, which was its initial state of motion, and therefore it slid forward off the seat.

Definition: Inertia is the property of an object due to which it tends to continue its state of rest or motion. Inertia is resistance to change the state. When a bus starts moving, the passengers feel a backward jerk because the lower part of the body moves along the motion of the bus, while the upper part of the body tends to stay at its initial position. On the other hand, when we stop pedaling our bicycle, it does not stop at once. The bicycle continues moving. However, the road’s friction and air resistance act against its motion and bring it to rest after some time.

Q.8: State the second law of motion and derive its expression.

Ans: Second Law of Motion:

Newton’s second law of motion describes the relationship between force and acceleration. Newton’s second law of motion states that:

“When a net force acts on a body, it produces acceleration in the direction of the force. The acceleration is directly proportional to force and inversely proportional to the mass of the body.”

Therefore,

$$a \propto F \quad \text{and} \quad a \propto \frac{1}{m}$$

Combining the above equations, we get:

$$a \propto \frac{F}{m}$$

Putting the proportionality constant $k$, we get:

$$a = k \frac{F}{m}$$ $$Fk = ma$$

Taking the value of constant $k = 1$, therefore:

$$F = ma$$

Q.9: Define mass and weight.

Ans: Mass:

Mass is the amount of matter present in a body. Mass is the actual amount of material contained in a body and is measured in kg. It is independent of everything. It is an intrinsic property of the body and remains the same wherever the body might be.

Weight:

Weight is the force exerted by gravity on that object ($w = mg$). Weight is a force (Force = mass × acceleration). The weight of an object is the mass times the acceleration due to gravity. It is a measure of how strongly gravity pulls on that matter. It is different on the earth, moon, and other places due to the difference in gravitational pull.

For example, objects weigh lesser on the moon where gravity is lower as compared to that on the Earth.

Q.10: State and explain Newton’s Third law of motion.

Ans: Newton’s Third Law of Motion:

This Law describes what happens when a body exerts a force on another body.

Definition: Newton’s third law of motion can be defined as:

"To every action, there is an equal and opposite reaction."

Examples:

1. Many times we throw a ball towards a wall and it bounces back. If it is thrown with greater force, the ball is returned with a greater push. It is because the wall reacts against the action of the ball.
2. While walking on the ground, we push the ground with our feet, and the ground pushes us back; thus, we move.

Action and Reaction Forces:

Action and reaction forces always occur in pairs, so when one body pushes against another, the second body pushes back just as hard. For example, when we put a book on a table, the book pushes the table downward, and the table pushes back the book upward. The action and reaction are forces that occur together as a pair. They are always equal in quantity but opposite in direction. While standing on the ground, gravity pulls you down against the ground, and the ground pushes up against your feet. When a rocket ignites its fuel behind it, the expanding exhaust gas pushes on the rocket, causing it to accelerate.

Q.11: What is the role of force according to Newton’s second law of motion?

Ans: According to Newton’s second Law of motion, a force is a vector that causes an object with mass to accelerate. Newton’s second Law states that the acceleration of an object depends upon two variables - the net force acting on the object and the mass of the object. The acceleration of the body is directly proportional to the net force acting on the body and inversely proportional to the mass of the body. This means that as the force acting upon an object is increased, the acceleration of the object is increased. Likewise, as the mass of the object is increased, the acceleration of the object is decreased.

Q.12: Describe uniform circular motion.

Ans: Uniform Circular Motion:

We take a smaller bucket, tie a piece of string to its handle. We hold the other end of the string and rotate the bucket in a vertical circle. We may feel some pull on your arm. Now we put a few coins in the bucket and again rotate it. It is amazing the coins do not fall even when the bucket goes bottom up. More interesting will be experimenting with some water. We pour about a cup of water into the bucket. Now we try rotating the bucket around and up. The water stuck to the bottom of the bucket. The force that keeps it stuck is known as centrifugal force and the force we apply against the pull on our arm is known as centripetal force.

Q.13: What happens according to Newton’s third law, while you pull a catapult?

Ans: “An object at rest stays at rest until a force is applied, and an object in motion stays in motion at the same speed, until a force acts upon it”.

An object at rest stays at rest; this means that the projectile will always sit in the cap if we don’t apply a force to it. Until a force is applied, the force we applied was the arm of the catapult. When we pull back the arm, it stores up a lot of energy, but when we let go of the arm, it changes the form of energy and applies a force to the projectile. This change in the energy created a force that launched the projectile forward.

Q.14: Define centripetal force.

Ans: Centripetal Force:

The force required to move a body along a circular path is called centripetal force. It is denoted by F. The centripetal force is always directed towards the center of the circular path. It depends on three factors:

1. The velocity of the object “v”
2. The object’s distance from the center “r”
3. The mass of the object “m”

It is given by the relation:

$$Fc = \frac{mv^2}{r}$$

Where:

• $m$ = mass of the body moving in circle
• $v$ = velocity of the body
• $r$ = radius of the circle

The velocity of the object is constant and perpendicular to a line running from the object to the center of the circle.

Q.15: Define centrifugal force.

Ans: Centrifugal Force:

Centrifugal force is the tendency of an object to leave the circular path and fly off in a straight line. Thus, it is defined as:

• A force that acts outward on a body that moves along a curved path is called centrifugal force.
• It is always directed away from the center of curvature.
• The magnitude of centrifugal force is equal but opposite in direction to centripetal force.

Q.16: Write few applications of the centrifuge.

Ans: Application of Centrifuge:

Centrifuge appliances are used to separate heavier particles from lighter particles in liquids, e.g., sugar crystals are separated from molasses. Blood analysis is carried out through a centrifuge process in a laboratory. A cream separator is used to separate the cream from skimmed milk. An ultracentrifuge is used for separating small particles from large molecules. A gas centrifuge is used for the separation of isotopes.

1. Road Banking: The outer edge or bank of the road is raised to a certain height at the curved part of roads. This provides the centripetal force against the type of the vehicle, hence prevents from skidding.

2. Cream Separator: The milk plants in the country are using high-speed spinners to separate cream from milk. The skimmed milk is heavier, whereas the cream is lighter. When the milk is spun at high speed, the heavy particles are pushed towards the walls of the spinner. These particles push the lighter particles of cream to the center, wherefrom it is collected through a tube.

3. Dryer: Nowadays, built-in dryer is available in most washing machines. It spins the wet clothes; hence, the water droplets are thrown away from the perforated walls of the dryer, and clothes get dry instantly.

Q.17: Which force prevents a passenger from falling down a roller coaster while it turns the riders into an upside-down position?

Ans: Inertia is what keeps us from falling out. Inertia is a resistance against a change in direction. It keeps us pressed against the bottom of the car with a force stronger than gravity.

Q.18: Define friction. Write down its expression and on what factors it depends?

Ans: Introduction of Friction:

When we throw a ball, it comes to rest after covering some distance. When we kick a ball and a box with the same force, the ball covers more distance than a box. We know that friction helps us walk easily, it prevents us from sliding, but sometimes it has disadvantages as well.

Definition of Friction:

The force that resists relative motion between two surfaces is called friction.

It is a contact force caused by the roughness or deformation of the materials in contact. The frictional force between a wooden block and cemented floor caused by the roughness of both the surfaces is projected in the given figure. Frictional forces are always parallel to the plane of contact between two surfaces and opposite to the direction of the applied force.

Expression of Friction:

Friction is a self-adjusting force. It can increase to a certain value known as Limiting force ($F_s$).

It is proportional to the normal force $R$.

$$F_s \propto R$$

The ratio between limiting force and normal reaction $R$ is constant, represented by the coefficient of friction $\mu$.

$$F_s = \mu R$$

or

$$\mu = \frac{F_s}{R}$$

When a body is placed on a surface, its weight $w$ acts downward. According to Newton’s third law of motion $R = W$, where $w = mg$. By putting the value $R = mg$ in the equation, $F_s = \mu R$, we get:

$$F_s = \mu mg$$

The coefficient of friction has different values for different surfaces as shown in the given table.

Q.19: Write down the different types of friction.

Ans: Types of Friction:

1. Static Friction: It is a force acting on an object at rest that resists its ability to start moving. The maximum static friction is known as "Limiting friction."

2. Kinetic Friction: It is the force that resists the motion of a moving object. It is interesting to know that in almost all situations, static friction is greater than kinetic friction.

3. Sliding Friction: When one body slides over the other body, the friction between two surfaces is said to be sliding friction.

4. Rolling Friction: When a body moves on wheels, the friction is said to be rolling friction. Rolling friction is much lesser than sliding friction.

Q.20: Write down a few advantages of friction.

Ans: Advantages of Friction:

1. Friction enables one to walk on the ground.

2. Friction protects from sliding, as sand is thrown to maintain friction on inclined railway tracks during rain.

3. The car brakes slow down the car to stop safely.

4. Threads and grooves are designed on tires to increase the friction and improve grip between road and wheel.

5. Now vehicles are equipped with Anti-Lock Braking System (ABS). ABS is designed to maintain steering stability, improve vehicle control, avoid skidding, and decrease stopping distances on dry and slippery surfaces. The ABS maintains the static friction as the wheel starts slipping; it releases the brake automatically for a fraction of a second, then holds the wheel again to create static friction between road and tires.

Q.21: What are the few disadvantages of friction?

Ans: Disadvantages of Friction:

1. A large amount of energy is wasted in the machines due to friction.
2. Friction leads to wear and tear of parts, hence increases the service cost.
3. Failure of the oil pump in a car engine results in contact between dry metals, which yields high temperature; hence the car engine is seized.

Q.22: Describe some ways to reduce friction.

Ans: Ways to Reduce Friction:

Wheels, pulleys, ball bearings, lubricants, and graphite are used to overcome friction. Lubricating the motor axle, sewing machine, and bicycle chain reduces friction and prevents wear and tear. The shape of the vehicle is also designed to reduce air resistance.

Q.23: When a free-falling object moves towards Earth due to the pull of the Earth on it, does Earth also move towards that object due to reaction? Explain.

Ans:

This can be easily explained by the equation of Newton’s second law of motion, $F = ma$. Earth and any other body pull each other towards each other. The force applied on both of them remains the same, but the changes in the position of an object are determined by its velocity and acceleration. Assume the mass of Earth to be $M$ and that of the arbitrary body to be $m$. Now, the force on both of these objects is $GMm / r^2$, where $r$ is the separation between these objects. The acceleration of these bodies is:

• Earth: $Gm / r^2$
• Body B: $GM / r^2$

If we try putting in values (as $G$ is very small), the Earth’s acceleration remains a very minute, ignorable quantity until the mass of $B$ becomes significantly large, comparable to planetary masses.

On the other hand, the acceleration of $B$ is considerably high, and hence we can observe its position changes with respect to time. If $B$ was something as heavy as the Sun, we would have been able to see the change in Earth’s position as we experience Earth revolving.

Q.24: Enlist any four uses of rolling friction in everyday life.

Ans: Any ball or wheel has rolling friction when rolled on a surface. Some uses of rolling friction include:

1. Truck, car, and skateboard tires
2. Rolling of ball bearings
3. Bike wheels
4. Rolling pin
5. Roller skate wheels

Q.25: Explore the following phenomenon relation with dynamics:

(a) When an air-filled balloon is released.
(b) The biker riding in the death well.

(a) When an air-filled balloon is released:

Ans: To help understand the forces acting on a balloon, use a free body diagram. A free-body diagram is a drawing that shows the forces and directions acting on an object. Below is a free-body diagram of a hot-air balloon. Buoyancy or Lift is created when the temperature in the balloon is increased, causing the density of the air to decrease. The less-dense (lighter) air inside the balloon tends to float on the more dense (heavier) air on the outside of the balloon. That is why hot-air balloons are referred to as lighter-than-air vehicles. If the amount of Lift is greater than the force of gravity acting on the mass of the balloon, then the balloon will rise. Warmer air inside the balloon will also cause the pressure inside the balloon to increase. The pressure inside the balloon will be greater than that on the outside of the balloon. For the balloon to maintain its shape, this force has to be greater than the forces acting in the opposite directions (pushing inward on the balloon). In hot-air balloons, drag is the friction that occurs as the balloon rises and moves through the surrounding air. Friction occurs between the moving balloon and the molecules of air, it hits as it rises. Both drag and the force of gravity acting on the mass of the balloon act in a downward force in opposition to the Lift. If the Lift is greater than the drag and force of gravity, then the balloon rises. If the Lift is less than the drag and the force of gravity, then the balloon descends. If the lifting force is equal to the force of drag and gravity, then the balloon will neither rise nor fall. For the purpose of illustration, there is no wind shown in the figure. However, wind can also act as a force on the balloon. The wind can come from nearly any direction and will tend to move the balloon in the direction it is blowing.

(b) The biker riding in the death well

Ans: When a bike moves on the walls, there are a number of forces in play. These include the gravitational force, which acts downward from the bike to the walls, the frictional force that the walls exert against the tires of the bike, and the normal reaction force, a perpendicular push back by the wall surface when it receives a force. There is also centripetal force, which is directed towards the center of the circular path that the bike traces. For a bike moving in a horizontal circle on a vertical wall, the normal reaction (N) is the factor that supplies enough force to sustain motion in a circle. Also, the fact that the bike does not slide down the wall signifies that the forces of friction and gravitation balance each other out (as shown in the figure above).

In short, the two forces, the gravitational force and the force of friction act in opposite directions and compensate each other, while the normal reaction from the wall is what keeps the bike moving. However, it’s not that simple. The frictional force exerted on the tires of the bike depends on the speed of the bike as it moves along the circle. This means that there has to be a minimum velocity of the bike that produces the maximum frictional force, effectively balancing out the gravitational force. This is why the rider must maintain a certain speed to stay balanced while riding in the death well.

The concept is crucial because if the gravitational force is greater, then the bike will slide down and the rider will fall off. The friction becomes stronger as the speed increases, but with increasing speed, it becomes more and more difficult for the rider to steer the vehicle safely. The above system of forces holds true and stays in equilibrium if we’re talking about a point mass, or rather, an object whose entire mass is concentrated in a single point. In such a case, all the forces are acting on that single point. This, however, is not the case with a motorbike. The frictional force is acting on the tires, but the gravitational force is acting through the center of mass of the system consisting of both the bike and the rider. Since the three forces are balanced but do not lie in the same line, the bike will tend to rotate, producing a turning effect that will eventually lead to it falling off. This anomaly has to be compensated for to keep these brave riders safe!

In order to counter this dangerous turning effect, the rider has to lean at an angle away from the vertical. This will make the normal reaction from the wall produce a tendency to rotate (a torque) in the opposite direction. If the rider bends at the correct angle, the torques will be perfectly balanced out; therefore, there will be no rotating or turning effect on the bike and the impressive display can continue.

However, if the rider leans at an angle other than the correct one, then the unbalanced torques will cause the bike to rotate and fall. Therefore, the rider will have to push harder in the opposite direction to supply extra torque and maintain his balance.