Common forces in mechanics MCQ Quiz - Objective Question with Answer for Common forces in mechanics - Download Free PDF

Calculation:

The forces on block m₁ are: its weight m₁g, normal reaction from the inclined plane N₁, and the reaction from block m₂ as R.

The forces on block m₂ are: m₂g, N₂, R, and the frictional force f.

If θ is slowly increased, f starts increasing and reaches its maximum value f = μN₂ at θ = θr (angle of repose).

From Newton’s second law:

f = μN₂

R = m₁g sin θ

N₁ = m₁g cos θ

f = R + m₂g sin θ

N₂ = m₂g cos θ

Solving these, we get the angle of repose:

θr = tan−1[(μ × m₂) / (m₁ + m₂)] = tan−1[(0.3 × 2) / (1 + 2)] = tan−1(0.2) = 11.5°

So:

For θ = 5° and θ = 10°, blocks are at rest with frictional force:

f = R + m₂g sin θ = (m₁ + m₂)g sin θ

For θ = 15° and θ = 20°, blocks are moving with frictional force:

f = μN₂ = μm₂g cos θ

Calculation:
According to Newton's third law, the force just enough to start the body moving must be equal to the force of static friction. And, according to Amontons' laws of friction,

F = F_{friction, static}

F_{friction, static} = μ_static N

N - mg = 0 (y-axis projection)

N = mg

F_{friction, static} = μ_static mg

F = μ_static mg

According to Newton's second law,

F - F_{friction, dynamic} = ma (x-axis projection)

F_{friction, dynamic} = μ_dynamic N

N - mg = 0 (y-axis projection)

N = mg

F_{friction, dynamic} = μ_dynamic mg

F - μ_dynamic mg = ma

μ_static mg - μ_dynamic mg = ma

a = g (μ_static - μ_dynamic)

a = 9.8 (0.6 - 0.4)

a = 1.96 m/s²

CONCEPT:

→The normal force in the circular track of radius R is written as;

 \(N = \frac{mv^2}{\mu R}\)

Here N is normal, m is the mass, R is the radius and v is the velocity.

CALCULATION:

A car of mass m is traveling on a flat track in a circular arc of radius R with a speed v, the free body diagram is shown below;

From the diagram we have;

\(mg +F_L = N\)   ----(1)

Ad we know, \(N = \frac{mv^2}{\mu R}\)

By putting the values of N in equation (1) we have;

\(mg +F_L = \frac{mv^2}{\mu R}\)

⇒ \(F_L = \frac{mv^2}{\mu R}-mg\)

⇒ \(F_L = m(\frac{v^2}{\mu R}-g)\)

Hence, option 3) is the correct answer.

Solution:

The block comes to rest after traveling a distance of 20 m. We can use the work-energy principle to find the frictional force. The work done by the frictional force is equal to the change in kinetic energy of the block.

The initial kinetic energy (K.E.) of the block is given by:

K.E. = (1/2) × m × v² = (1/2) × 20 × (10)² = 1000 J

The work done by the frictional force is:

W = F × d

Where F is the frictional force and d is the distance traveled (20 m). Since the block comes to rest, all the kinetic energy is used up by the frictional force. Therefore:

1000 J = F × 20

Solving for F:

F = 1000 / 20 = 50 N

Hence, the magnitude of the frictional force is 50 N (Option 4).

Given:

A block of mass m is placed on a rough inclined plane at an angle of 30° with the horizontal. Coefficients of static friction (μ_s) and kinetic friction (μ_k) are 0.6 and 0.5, respectively. The gravitational acceleration g = 10 m/s². We need to calculate the acceleration of the block.

Concept:

• The forces acting on the block are:
  • Gravitational force along the incline: mgsinθ.
  • Normal reaction force perpendicular to the incline: mgcosθ.
  • Frictional force opposing motion:
    • Static friction: f_s ≤ μ_smgcosθ.
    • Kinetic friction: f_k = μ_kmgcosθ.
• The block will remain stationary if the static friction is sufficient to balance the gravitational force along the incline:

  f_s ≥ mgsinθ.

• If mgsinθ > μ_smgcosθ, the block will move, and the net acceleration can be calculated as:

  a = gsinθ - μ_kgcosθ.

Calculation:

Calculate mgsinθ and μ_smgcosθ:

mgsinθ = m × 10 × sin30° = m × 10 × 0.5 = 5m.

μ_smgcosθ = μ_s × m × 10 × cos30° = 0.6 × m × 10 × 0.866 = 5.196m.

Compare mgsinθ and μ_smgcosθ:

Since mgsinθ (5m) < μ_smgcosθ (5.196m), the static friction is sufficient to prevent motion.

Determine acceleration:

The block does not move, so its acceleration is 0 m/s².

∴ The acceleration of the block is zero.

The correct answer is The friction between the feet and the path is reduced.

Important Points

• Friction is a force between two surfaces that are sliding, or trying to slide, across each other.
  • For example, when you try to push or pull luggage along the floor, friction makes this difficult.
• Friction always works in the opposite of the direction in which the object is moving or trying to move.
• There are four types of friction:
  • Static Friction: Static friction acts on objects when they are resting on a surface.
    • For example, hiking in the woods, there is static friction between shoes and the trail each time put down the foot.
    • Without this static friction, feet would slip out and making it difficult to walk.
  • Sliding Friction: Sliding friction is friction that acts on objects when they are sliding over a surface.
    • Sliding friction is weaker than static friction.
  • Rolling Friction: Rolling friction is friction that acts on objects when they are rolling over a surface.
    • Rolling friction is much weaker than sliding friction or static friction.
    • For example, ground transportation use wheels, including bicycles, cars, 4-wheelers, roller skates, scooters, skateboards, Ball bearings.
  • Fluid Friction: Fluid friction is friction that acts on objects that are moving through a fluid.
    • A fluid is a substance that can flow and take the shape of its container. Fluids include liquids and gases.

Concept:

Friction Force:

It is a kind of resisting force that acts between two contact bodies to avoid relative motion between them.

• It is formed due to the close interaction of charged particles at the surface of the bodies due to electromagnetic forces.
• Mathematically it is represented as Friction force = μ N.
• Where N = normal force = m × g
• Normal force: It is a force that is exerted by the surface perpendicular to the body. It is a component of the contact force.

Frictional forces are of two kinds:

1. Static friction (f_s): When two bodies do not slip on each other, the force of friction is static friction. It can change its value until its max. F_max ≥ f_s
2. Kinetic Friction (f_k): When two bodies slip over each other the force of friction is called kinetic friction.

• Coefficient of Kinetic friction (μ_k) < Coefficient Static friction (μ_s).

• Here, Applied force = friction force
• Applied force (F) = μ N = μ m g

Explanation:

• Since the block does not move so frictional force (f_s) ≥ Applied force
• This means frictional force (f_s) ≥ 200 N

The correct option is Static friction > Kinetic friction > Rolling friction.

Key Points

• Friction: The motion of any object is resisted by an opposing force known as the force of friction.
• The rolling friction is very low as compared to the other two frictions.
• If we compare kinetic and static friction then the value of static friction is more because it is present when the motion is not started after overcoming this friction object is able to move.
• Static friction > Kinetic friction > Rolling friction

Additional Information

Friction is of three types:

• Static Friction: The friction force encountered when the object is in the rest position that's static friction.
• Kinetic Friction: If the object is sliding against each other then the friction present at that time is kinetic friction.
• Rolling Friction: If the object is rolling on the surface the friction which is present at that time between the surfaces is known as Rolling friction.

CONCEPT:

Pseudo Force:

• A Pseudo force (also called a fictitious force, inertial force, or d’Alembert force) is an apparent force that acts on all masses whose motion is described using a non-inertial frame of reference frame, such as a rotating reference frame.
• Pseudo force comes in effect when the frame of reference has started acceleration compared to a non-accelerating frame.

​EXPLANATION:

• A person having mass m is standing on a weighing machine which is placed in a stationary lift. In this case, the actual weight of a person is mg.
• This weight on that weighing machine offers a normal reaction N, which is nothing but the reading of the weighing machine.
• This reaction exerted by the weighing machine on the man is the apparent weight of the man.
• This apparent weight depends upon the motion of the lift.

​Case 1 :

• When the lift is at rest or moving with a uniform velocity no matter upwards or downwards, the apparent weight of the man is given as,

​⇒ N = mg i.e., the actual weight of a man.

Case 2 :

• When the lift accelerates upwards with an acceleration a, the apparent weight is given as,
• ​From FBD we can see that,

⇒ N - mg = ma

⇒ N = m(g + a)

• In this case, the apparent weight of the man has become more than the actual weight.

​Case 3 :

• When the lift accelerates downward with an acceleration a, the apparent weight is given as,
• ​From FBD we can see that,

⇒ mg - N = ma

⇒ N = m(g - a)

• In this case, the apparent weight of the man has become less than the actual weight. Hence, option 2 is correct.​

CONCEPT:

Friction:

• The resistance offered by the surfaces that are in contact with each other when they move over each other is called friction.
• Factors affecting friction:
  1. Types of surfaces in contact.
  2. The normal force between the two surfaces.
• Friction force does not depend on the velocity of the object.

Limiting friction:

• The maximum friction that can be generated between two static surfaces in contact with each other.
• Once a force applied to the two surfaces exceeds the limiting friction, the motion will occur.
• We know that the limiting friction force between any two surfaces is given as,

⇒ F = μN

Where F = friction force, μ = coefficient of friction and N = normal reaction

Newton's second law of motion:

• According to Newton's second law of motion, the rate of change of momentum of a body is directly proportional to the applied unbalanced force.
• The magnitude of the force is given as,

⇒ F = ma

Where m = mass and a = acceleration

CALCULATION:

Given:

 m = 20 kg, μ = 0.5, P = 40 N, t = 10 sec and g = 10 m/sec2

​Since the body is resting on a rough horizontal plane so the normal reaction is given,

⇒ N = mg

⇒ N = 20 × 10

⇒ N = 200 N

The limiting friction is given as,

⇒ F = μN

⇒ F = 0.5 × 200

⇒ F = 100 N

• Since the applied force is less than the limiting friction so the body will remain at rest. Hence, option 3 is correct.

CONCEPT:

• Sir Isaac Newton gave us the concept of force.
• Force is a stimulus provided to an object in order to make it do something.
• Force can be both against the motion and for it.
• The amount of force required is related to the mass of the object, the greater the mass, the greater the force required to move it. 

There are two types of forces based on their applications:

1. Contact Force - It is a force applied to a body by another body that is in contact with it.

• eg: Muscular Force, Mechanical Force, Frictional Force

1. Non-Contact Force - It is a force that acts on an object without coming physically in contact with it.

• eg: Gravitational Force, Electrostatic force, Magnetic force

EXPLANATION:

• Force of gravity (GRAVITATIONAL FORCE):  This force is a force that attracts any two objects with mass.
  • Gravitational force is attractive because it always tries to pull masses together, it never pushes them apart. In fact, every object, including you, is pulling on every other object in the entire universe. This is called Newton's Law of Gravitation.
• Magnetic force:
  • ​Attraction or repulsion that arises between electrically charged particles because of their motion.
  • It is the basic force responsible for such effects as the action of electric motors and the attraction of magnets for iron.
• Electrostatic force: It is also known as the Coulomb force or Coulomb interaction. It's an attractive or repulsive force between two electrically charged objects. Like charges repel each other while unlike charges attract each other. Coulomb's law is used to calculate the strength of the force between two charges.

CONCEPT:

• Circular motion: When a body moves in such a way that its force is always perpendicular to the velocity, the motion will be circular motion.
• Centripetal force: The force that is perpendicular to the velocity and directed towards the center is known as centripetal force. or
  • The force that makes a body move in a circular motion is known as centripetal force.
  • The direction of this force is always perpendicular to the direction of the velocity.

The centripetal force acting on a body of mass 'm' revolving with radius 'r' is:

\(F = {mv^2\over r}\)

EXPLANATION:

Given that applied force is uniform and perpendicular to the motion.

• From the definition of the centripetal force, if a force is perpendicular to the motion, it is a centripetal force and this force makes the body move in a circular motion.

We know \(F = {mv^2\over r}\)

• Since F is uniform, so v will also be uniform. So speed (magnitude of velocity) will not change.
• In a circular motion, a body moves in a circle, and in a circle the direction of motion changes at every point.

• At point A, the direction of the velocity is in the upward direction. 
• At point B, the direction of the velocity is in the leftward direction,
• At point C, the direction of the velocity is in the downward direction.

• The body comes in the initial direction after one complete circle.
• So If the force on a moving body is always uniform and perpendicular to its motion, then Speed remains the same, but direction changes.
• Hence the correct answer is option 4.

The correct answer is Only I

• The friction force is a contact force.
• Contact force is a force that is applied by objects in contact with each other.
• The contact force is governed by Newton’s Laws.
• Friction is the resistance to motion of one object moving relative to another.
• Magnetic force is the non-contact force.
• Gravitation force is also a non-contact force.

Types of contact forces:

• Frictional Force
• Applied Force
• Normal Force

CONCEPT:

• Friction is the resistance force that opposes relative motion between two objects. 
  • It is not a fundamental force, like gravity or electromagnetism.
  • The direction of friction is always in such a way that it opposes the relative motion
• The friction force between two surfaces is due to the roughness of the contact surface.

EXPLANATION:

• The friction force between two surfaces is due to the roughness of the contact surface.
• When the surfaces are polished, their roughness decreases.
• They become smooth.
• Hence the friction between them decreases.
• So the correct answer is option 2.

CONCEPT:

Friction Force: It is a kind of resisting force that acts between two contact bodies to avoid relative motion between them.

• It is formed due to the close interaction of charged particles at the surface of the bodies due to electromagnetic forces.
• Mathematically it is represented as Friction force = μ N.
• Where N = normal force = m × g
• Normal force: It is a force that is exerted by the surface perpendicular to the body. It is a component of the contact force.

Frictional forces are of two kinds:

1. Static friction (f_s): When two bodies do not slip on each other, the force of friction is static friction. It can change its value until its max. F_max ≥ f_s
2. Kinetic Friction (f_k): When two bodies slip over each other the force of friction is called kinetic friction.

• Coefficient of Kinetic friction (μ_k) < Coefficient Static friction (μ_s).

• Force: It is a kind of push or pull of a body.
  • Force produces acceleration in a body.
  • F = m × a [m = mass of the body, a = acceleration in a body]
• Free Body Diagram: It is an illustration to visualize the forces and resultants of each body respectively

CALCULATION:

• Given, Mass of the body (m) = 10 kg, Normal force = mg = 10 × 10 = 100 N
• Coefficient of friction (μ) = ?
• Free body diagram of the box is

Since the body accelerates in the direction of the force.

The laws of motion in the horizontal line is

F - μ_k N = ma

⇒ 50 – (μ_k × 100) = 10 kg × 2 m/s²

⇒ μ _k = 0.3

Since the body is already in motion the kinetic friction is working.