3 questions about Friction force equation

1. Block A 3 kg is placed on the table and then tied to a rope that is connected to stone B = 2 kg through a pulley as shown. The mass and friction of the pulleys are neglected. Acceleration due to gravity g = 10 m/s^{2}. Determine the acceleration of the system and the tension in the rope if:

a) smooth table

b) rough table with a coefficient of kinetic friction of 0.4

__Known:__

The mass of block A (m_{A}) = 3 kg

The mass of rock B (m_{B}) = 2 kg

Acceleration due to gravity (g) = 10 m/s^{2}

Weight of block A (w_{A}) = m g = (3)(10) = 30 Newton

Weight of rock B (w_{B}) = m g = (2)(10) = 20 Newton

__Wanted:__ The acceleration of the system (a) and the tension in the rope (T)

__Solution:__

*a) smooth table*

**Calculate the acceleration of the system using the formula for Newton’s second law:**

ΣF = m a

w_{B} = (m_{A} + m_{B}) a

20 = (3 + 2) a

20 = 5 a

a = 20 / 5 = 4 m/s^{2}

**Calculate the tension in the rope using the formula for the tension in the rope:**

**The tension in the rope on block A:**

ΣF = m_{A} a

T = m_{A} a = (3)(4) = 12 Newton

**The tension in the rope on block B:**

ΣF = m_{B} a

w_{B} – T = (2)(4)

20 – T = 8

T = 20 – 8 = 12 Newton

*b) rough table with a coefficient of kinetic friction of 0.4*

The force of the kinetic Friction:

F_{k} = µ_{k} N = (0,4)(30) = 12 Newton

**Calculate the acceleration of the system using the formula for Newton’s second law:**

ΣF = m a

w_{B} – f_{k} = (m_{A} + m_{B}) a

20 – 12 = (3 + 2) a

8 = 5 a

a = 8 / 5 = 1,6 m/s^{2}

**Calculate the tension in the rope using the formula for the tension in the rope:**

The tension in the rope on block A:

ΣF = m_{A} a

T – fk = m_{A} a

T – 12 = (3)(1,6)

T – 12 = 4,8

T = 4,8 + 12 = 16,8 Newton

The tension in the rope on block B:

ΣF = m_{B} a

w_{B} – T = (2)(1,6)

20 – T = 3,2

T = 20 – 3,2 = 16,8 Newton

2. An object with a mass of 10 kg is in a horizontal plane. The coefficient of static friction is 0.4 and the coefficient of kinetic friction is 0.35. g = 10 m/s^{2}. If an object is given a constant horizontal force of 25 N, the magnitude of the frictional force acting on the object is…

__Known:__

The mass of the object (m) = 10 kg

The coefficient of Static friction (µ_{s}) = 0.4

The coefficient of kinetic friction (µk) = 0.35

Acceleration due to gravity (g) = 10 m/s^{2}

Horizontal force (F) = 25 N

The object’s gravity (w) = m g = (10)(10) = 100 Newton

Normal force (N) = w = 100 Newton

__Wanted:__ The amount of static friction (f_{s}) and kinetic (f_{k})

__Solution:__

The force of the static Friction::

f_{s} = µ_{s} N = (0,4)(100) = 40 Newton

The force of the Kinetic Friction:

f_{k} = µ_{k} N = (0,35)(100) = 35 Newton

The horizontal force is only 25 Newton so it can’t move objects yet.

3. The masses of blocks A and B in the figure are 10 kg and 5 kg respectively. The coefficient of friction between block A and the plane is 0.2. To prevent block A from moving, the minimum mass of block C required is…

__Known:__

The mass of block A (m_{A}) = 10 kg

The mass of block B (m_{B}) = 5 kg

Coefficient of static friction of block A (µ_{s}) = 0,2

Gravity acceleration (g) = 10 m/s^{2}

Block weight A (w_{A}) = m_{A} g = (10)(10) = 100 Newton

Block weight B (w_{B}) = m_{B} g = (5)(10) = 50 Newton

Static friction (f_{s}) = µ_{s} N = (0,2)(w_{A} + w_{C}) = (0,2)(100 + w_{C}) = 20 + 0,2 w_{C}

__Ditanya:__ The mass of block C to keep the system at rest

__Jawab:__

The system is at rest so the formula for Newton’s first law is used:

ΣF = 0

w_{B} – f_{s} = 0

50 – (20 + 0,2 w_{C}) = 0

50 – 20 – 0,2 w_{C} = 0

30 – 0,2 w_{C} = 0

30 = 0,2 w_{C}

w_{C }= 30 / 0,2 = 300 / 2 = 150 Newton

The mass of block C = 150 / 10 = 15 Kg

**20 conceptual questions and answers related to friction force.**

**Question:**What is friction?**Answer:**Friction is a force that opposes motion between two surfaces that are in contact.**Question:**How is the force of friction calculated?**Answer:**The force of friction is calculated as the product of the friction coefficient and the normal force: f = μN.**Question:**What are the types of friction?**Answer:**The main types of friction are static friction, kinetic friction, and rolling friction.**Question:**What is the difference between static and kinetic friction?**Answer:**Static friction prevents an object from starting to move, while kinetic friction acts on an object that is already in motion.**Question:**What is the coefficient of friction?**Answer:**The coefficient of friction is a scalar value that describes the ratio of the force of friction between two bodies and the force pressing them together.**Question:**Can the coefficient of friction be greater than 1?**Answer:**Yes, the coefficient of friction can be greater than 1. It depends on the materials of the two surfaces in contact.**Question:**Why does an object in motion experience a friction force in the opposite direction?**Answer:**The friction force acts in the opposite direction to oppose the motion or potential motion of the object, reducing its speed or preventing it from starting to move.**Question:**How does the force of friction change with the mass of an object?**Answer:**The force of friction is directly proportional to the mass of the object. If the mass increases, the frictional force also increases, assuming a constant gravitational field and no change in the coefficient of friction.**Question:**What is the unit of the frictional force?**Answer:**The SI unit of frictional force is the Newton (N), which is equivalent to 1 kg x m/s².**Question:**Can there be friction in the absence of motion?**Answer:**Yes, static friction can exist even in the absence of motion. It prevents an object from starting to move.**Question:**Why does friction not depend on the area of contact?**Answer:**Friction doesn’t depend on the area of contact because it results from the interlocking of microscopic irregularities on the two surfaces. When the area of contact increases, these irregularities get spread out over a larger area, but the total force acting over the area remains the same.**Question:**What is rolling friction?**Answer:**Rolling friction is the force resisting the motion when an object rolls on a surface.**Question:**Is the force of friction always parallel to the surface of contact?**Answer:**Yes, the force of friction is always parallel to the surface of contact and opposite to the direction of motion or potential motion.**Question:**How does lubrication affect the friction between two surfaces?**Answer:**Lubrication reduces friction between two surfaces by creating a thin layer that separates the surfaces, which reduces the interlocking of microscopic irregularities.**Question:**How does friction convert kinetic energy?**Answer:**Friction converts kinetic energy to thermal energy due to the interactions at the molecular level between the two surfaces in contact.**Question:**Why does an object moving on a flat surface come to a stop even if no other force is acting on it?**Answer:**An object moving on a flat surface comes to a stop because of the force of friction, which acts in the opposite direction of motion and gradually reduces the object’s speed to zero.**Question:**How can you increase the frictional force between two surfaces?**Answer:**Friction can be increased by using materials that have a higher coefficient of friction, by increasing the mass of the object, or by increasing the roughness of the surfaces.**Question:**What role does friction play in walking?**Answer:**Friction is crucial for walking because it provides the force that allows our feet to push off the ground without slipping.**Question:**How is air resistance related to friction?**Answer:**Air resistance is a form of friction where the air particles oppose the motion of an object moving through the air.**Question:**Is friction always undesirable?**Answer:**No, friction is not always undesirable. While it can cause wear and heat generation, it’s also essential for many activities, like walking or driving, where it prevents slipping and allows movement.