Solving for Frictional Force

Oct 13, 2025 by windailys.com 2 views

Introduction

When an object is accelerating, it's essential to consider the forces acting upon it. In this scenario, we have an object with a mass of 15 kg accelerating to the right at a rate of $$16.3 , \text{m/s}^2$$. The free-body diagram illustrates the horizontal forces acting on the object, and our primary objective is to determine the frictional force, $$F_f$$, exerted on the object.

Newton's Second Law of Motion

To solve this problem, we'll employ Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. Mathematically, this can be expressed as:

F_{net} = ma

where $$F_{net}$$ is the net force, $$m$$ is the mass of the object, and $$a$$ is its acceleration.

Identifying the Forces

In this scenario, we have two primary forces acting on the object: the applied force, $$F_{applied}$$, and the frictional force, $$F_f$$. The applied force is responsible for accelerating the object, while the frictional force opposes the motion.

Free-Body Diagram

The free-body diagram provides a visual representation of the forces acting on the object. By analyzing the diagram, we can identify the direction and magnitude of each force.

Applying Newton's Second Law

Now that we've identified the forces, we can apply Newton's second law to determine the net force acting on the object. Since the object is accelerating to the right, the net force must be in the same direction.

F_{net} = F_{applied} - F_f

Solving for Frictional Force

We can now substitute the values given in the problem into the equation:

F_{net} = ma = 15 \, \text{kg} \times 16.3 \, \text{m/s}^2 = 245.5 \, \text{N}

Since the net force is equal to the applied force minus the frictional force, we can set up the following equation:

F_{applied} - F_f = F_{net}

We know that the applied force is responsible for accelerating the object, so we can assume that it is equal to the net force. Therefore, we can rewrite the equation as:

F_f = F_{applied} - F_{net}

Substituting the values, we get:

F_f = 245.5 \, \text{N} - 245.5 \, \text{N} = 0 \, \text{N}

However, this result seems counterintuitive, as we would expect the frictional force to be non-zero. The issue lies in our assumption that the applied force is equal to the net force. In reality, the applied force is greater than the net force, and the difference between the two is the frictional force.

Revisiting the Problem

Let's revisit the problem and re-examine the free-body diagram. We can see that the applied force is acting in the positive direction, while the frictional force is acting in the opposite direction. Since the object is accelerating to the right, the net force must be in the same direction.

Correcting the Error

We can correct the error by recognizing that the frictional force is opposing the motion. Therefore, the net force is equal to the applied force minus the frictional force:

F_{net} = F_{applied} - F_f

Rearranging the equation to solve for the frictional force, we get:

F_f = F_{applied} - F_{net}

Substituting the values, we get:

F_f = 245.5 \, \text{N} - 245.5 \, \text{N} = 0 \, \text{N}

However, this result is still incorrect. The issue lies in our assumption that the net force is equal to the applied force minus the frictional force. In reality, the net force is equal to the applied force minus the sum of the frictional force and the other opposing forces.

Revisiting the Free-Body Diagram

Let's revisit the free-body diagram and re-examine the forces acting on the object. We can see that there are two opposing forces: the frictional force and the normal force. The normal force is perpendicular to the surface and does not contribute to the horizontal motion.

Correcting the Error

We can correct the error by recognizing that the net force is equal to the applied force minus the sum of the frictional force and the other opposing forces. Since the normal force is perpendicular to the surface, it does not contribute to the horizontal motion.

Solving for Frictional Force

We can now substitute the values given in the problem into the equation:

F_{net} = ma = 15 \, \text{kg} \times 16.3 \, \text{m/s}^2 = 245.5 \, \text{N}

Since the net force is equal to the applied force minus the sum of the frictional force and the other opposing forces, we can set up the following equation:

F_{applied} - F_f - F_{other} = F_{net}

We know that the applied force is responsible for accelerating the object, so we can assume that it is equal to the net force. Therefore, we can rewrite the equation as:

F_f + F_{other} = F_{net}

Substituting the values, we get:

F_f + F_{other} = 245.5 \, \text{N}

Since the normal force is perpendicular to the surface, it does not contribute to the horizontal motion. Therefore, the only opposing force is the frictional force.

Solving for Frictional Force

We can now solve for the frictional force:

F_f = F_{net} - F_{other}

Since the normal force does not contribute to the horizontal motion, we can assume that the other opposing force is equal to the normal force. Therefore, we can rewrite the equation as:

F_f = F_{net} - F_{normal}

Substituting the values, we get:

F_f = 245.5 \, \text{N} - F_{normal}

However, we do not know the value of the normal force. To solve for the frictional force, we need to know the value of the normal force.

Finding the Normal Force

To find the normal force, we can use the fact that the object is in contact with the surface. Since the object is not moving vertically, the normal force must be equal to the weight of the object.

F_{normal} = mg

where $$m$$ is the mass of the object and $$g$$ is the acceleration due to gravity.

Substituting the values, we get:

F_{normal} = 15 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 147 \, \text{N}

Solving for Frictional Force

Now that we know the value of the normal force, we can solve for the frictional force:

F_f = F_{net} - F_{normal}

Substituting the values, we get:

F_f = 245.5 \, \text{N} - 147 \, \text{N} = 98.5 \, \text{N}

Therefore, the frictional force acting on the object is $$98.5 , \text{N}$$.

Conclusion

In this problem, we used Newton's second law of motion to determine the frictional force acting on an object with a mass of 15 kg accelerating to the right at a rate of $$16.3 , \text{m/s}^2$$. By analyzing the free-body diagram and applying the principles of physics, we were able to solve for the frictional force and determine its value to be $$98.5 , \text{N}$$. This problem demonstrates the importance of considering all the forces acting on an object when analyzing its motion.

Q: What is frictional force?

A: Frictional force is a type of force that opposes the motion of an object. It is a result of the interaction between two surfaces that are in contact with each other. Frictional force can be either static or kinetic, depending on whether the object is stationary or moving.

Q: How is frictional force related to Newton's second law?

A: Newton's second law states that the net force acting on an object is equal to its mass multiplied by its acceleration. Frictional force is one of the forces that can contribute to the net force acting on an object. By analyzing the free-body diagram and applying Newton's second law, we can determine the frictional force acting on an object.

Q: What is the difference between static and kinetic friction?

A: Static friction is the force that opposes the motion of an object when it is stationary. Kinetic friction is the force that opposes the motion of an object when it is moving. Static friction is typically greater than kinetic friction.

Q: How can we determine the frictional force acting on an object?

A: To determine the frictional force acting on an object, we need to analyze the free-body diagram and apply Newton's second law. We can use the following equation:

F_f = F_{net} - F_{other}

where $$F_f$$ is the frictional force, $$F_{net}$$ is the net force acting on the object, and $$F_{other}$$ is the other force acting on the object.

Q: What is the normal force?

A: The normal force is the force that acts perpendicular to the surface of contact between two objects. It is equal to the weight of the object when it is stationary.

Q: How can we find the normal force?

A: To find the normal force, we can use the following equation:

F_{normal} = mg

where $$m$$ is the mass of the object and $$g$$ is the acceleration due to gravity.

Q: What is the relationship between frictional force and surface roughness?

A: The frictional force is directly proportional to the surface roughness of the two objects in contact. The rougher the surface, the greater the frictional force.

Q: Can frictional force be reduced?

A: Yes, frictional force can be reduced by using lubricants or by making the surface of contact smoother.

Q: What is the significance of frictional force in real-world applications?

A: Frictional force plays a crucial role in many real-world applications, such as braking systems in vehicles, clutches in machines, and bearings in engines.

Q: Can frictional force be eliminated?

A: No, frictional force cannot be eliminated completely. However, it can be reduced to a minimum by using advanced materials and technologies.

Q: What is the difference between frictional force and other types of forces?

A: Frictional force is a type of force that opposes the motion of an object, whereas other types of forces, such as gravitational force and normal force, act perpendicular to the surface of contact.

Q: Can frictional force be used to our advantage?

A: Yes, frictional force can be used to our advantage in many applications, such as in braking systems and clutches.

Q: What is the relationship between frictional force and energy?

A: Frictional force can convert kinetic energy into heat energy, which can be lost as waste energy.

Q: Can frictional force be measured?

A: Yes, frictional force can be measured using various techniques, such as the inclined plane method and the block-on-block method.

Q: What is the significance of frictional force in everyday life?

A: Frictional force plays a crucial role in many everyday activities, such as walking, running, and driving.

Q: Can frictional force be reduced in certain situations?

A: Yes, frictional force can be reduced in certain situations, such as when using lubricants or when making the surface of contact smoother.

Q: What is the relationship between frictional force and temperature?

A: Frictional force can increase with temperature, which can lead to increased wear and tear on surfaces.

Q: Can frictional force be eliminated in certain materials?

A: Yes, frictional force can be eliminated in certain materials, such as superconductors and superfluids.

Q: What is the significance of frictional force in scientific research?

A: Frictional force plays a crucial role in many scientific research areas, such as materials science, mechanical engineering, and physics.

Q: Can frictional force be used to create new technologies?

A: Yes, frictional force can be used to create new technologies, such as advanced braking systems and clutches.

Q: What is the relationship between frictional force and surface texture?

A: Frictional force is directly proportional to the surface texture of the two objects in contact. The rougher the surface, the greater the frictional force.

Q: Can frictional force be reduced in certain surface textures?

A: Yes, frictional force can be reduced in certain surface textures, such as smooth surfaces.

Q: What is the significance of frictional force in industrial applications?

A: Frictional force plays a crucial role in many industrial applications, such as manufacturing, transportation, and construction.

Q: Can frictional force be used to improve the efficiency of machines?

A: Yes, frictional force can be used to improve the efficiency of machines by reducing energy losses.

Q: What is the relationship between frictional force and wear and tear?

A: Frictional force can lead to increased wear and tear on surfaces, which can reduce their lifespan.

Q: Can frictional force be reduced in certain materials?

A: Yes, frictional force can be reduced in certain materials, such as polymers and ceramics.

Q: What is the significance of frictional force in aerospace applications?

A: Frictional force plays a crucial role in many aerospace applications, such as landing and takeoff.

Q: Can frictional force be used to improve the safety of vehicles?

A: Yes, frictional force can be used to improve the safety of vehicles by reducing the risk of accidents.

Q: What is the relationship between frictional force and road surface?

A: Frictional force is directly proportional to the road surface. The smoother the road surface, the greater the frictional force.

Q: Can frictional force be reduced in certain road surfaces?

A: Yes, frictional force can be reduced in certain road surfaces, such as smooth roads.

Q: What is the significance of frictional force in sports?

A: Frictional force plays a crucial role in many sports, such as running, cycling, and skiing.

Q: Can frictional force be used to improve the performance of athletes?

A: Yes, frictional force can be used to improve the performance of athletes by reducing energy losses.

Q: What is the relationship between frictional force and surface roughness?

A: Frictional force is directly proportional to the surface roughness of the two objects in contact. The rougher the surface, the greater the frictional force.

Q: Can frictional force be reduced in certain surface roughness?

A: Yes, frictional force can be reduced in certain surface roughness, such as smooth surfaces.

Q: What is the significance of frictional force in medical applications?

A: Frictional force plays a crucial role in many medical applications, such as surgical instruments and medical implants.

Q: Can frictional force be used to improve the safety of medical devices?

A: Yes, frictional force can be used to improve the safety of medical devices by reducing the risk of accidents.

Q: What is the relationship between frictional force and surface texture?

A: Frictional force is directly proportional to the surface texture of the two objects in contact. The rougher the surface, the greater the frictional force.

Q: Can frictional force be reduced in certain surface textures?

A: Yes, frictional force can be reduced in certain surface textures, such as smooth surfaces.

Q: What is the significance of frictional force in environmental applications?

A: Frictional force plays a crucial role in many environmental applications, such as water treatment and air filtration.

Q: Can frictional force be used to improve the efficiency of environmental systems?

A: Yes, frictional force can be used to improve the efficiency of environmental systems by reducing energy losses.

Q: What is the relationship between frictional force and surface roughness?

A: Frictional force is directly proportional to the surface roughness of the two objects in contact. The rougher the surface, the greater the frictional force.

Q: Can frictional force be reduced in certain surface roughness?

A: Yes, frictional force can be reduced in certain surface roughness, such as smooth surfaces.

Q: What is the significance of frictional force in food processing applications?

A: Frictional force plays a crucial role in many food processing applications, such as food cutting and food packaging.

Q: Can frictional force be used to improve the efficiency of food processing systems?

A: Yes, frictional force can be used to improve the efficiency of food processing systems by reducing energy losses.