Question

If the block has a mass of \(2 \mathrm{~kg}\), and a pulling force of \(20 \mathrm{~N}\) acting on the block causes it to accelerate at \(4 \mathrm{~m} / \mathrm{s}^2\), what is the value of the frictional force acting on the block? (A) \(10 \mathrm{~N}\) (B) \(12 \mathrm{~N}\) (C) \(20 \mathrm{~N}\) (D) \(40 \mathrm{~N}\)

Short answer

The frictional force acting on the block is \(12 \mathrm{~N}\), which corresponds to option (B).

Step-by-step solution

Write down Newton's second law of motion

Newton's second law of motion states that the net force acting on an object (F_net) is equal to the mass of the object (m) multiplied by its acceleration (a). This can be written as: \(F_{\text{net}} = m \cdot a\)

Define the net force

The net force acting on the block is the difference between the pulling force (F_pull) and the frictional force (F_friction): \(F_{\text{net}} = F_{\text{pull}} - F_{\text{friction}}\)

Substitute the given values

We are given the mass of the block (m = 2 kg), the pulling force (F_pull = 20 N), and the acceleration of the block (a = 4 m/s²). We can substitute these values into the equation from Step 1 and Step 2: \(F_{\text{net}} = m \cdot a = F_{\text{pull}} - F_{\text{friction}}\) \(20 - F_{\text{friction}} = 2 \cdot 4\)

Solve for the frictional force

Now we can solve for the frictional force (F_friction): \(20 - F_{\text{friction}} = 8\) \(F_{\text{friction}} = 20 - 8 = 12 \mathrm{~N}\) The frictional force acting on the block is 12 N, which corresponds to option (B).

Key concepts

Newton's second law

Newton's second law of motion is a fundamental principle in physics that helps us understand how objects move when forces are applied to them. The law states that the net force acting on an object is equal to the mass of that object multiplied by its acceleration: \( F_\text{net} = m \cdot a \). This equation is crucial because it links force, mass, and acceleration in a very straightforward manner.

In practical terms, Newton's second law tells us that for an object to accelerate, a force must be applied. The greater the force, the greater the acceleration, assuming the mass remains constant. Similarly, the more massive an object is, the more force is required to achieve the same acceleration. This is why heavier objects need stronger pushes to move as quickly as lighter ones. If you're pushing a car or a toy, you'll notice the difference!

This principle not only helps in calculating forces but also in understanding how various forces interact. It serves as the backbone for many calculations you'll encounter in physics, such as those involving dynamics, momentum, and energy.

frictional force calculation

Frictional force is the resistive force that opposes the motion of an object. When calculating friction, we must consider all forces acting on the object, as it directly affects the net force in equations. In our problem, the frictional force is given by the difference between the pulling force and the net force.

To determine the frictional force, you would

• Calculate the net force using Newton's second law, \( F_\text{net} = m \cdot a \).
• Identify the applied force, which here is the pulling force.
• Use the equation \( F_\text{net} = F_\text{pull} - F_\text{friction} \) to find the frictional force by rearranging the formula: \( F_\text{friction} = F_\text{pull} - F_\text{net} \).

Understanding how to calculate friction helps in solving problems where resistive forces come into play. It explains why sometimes more force is necessary to keep an object moving or why objects slow down when you stop applying a force. Frictional forces play a massive role in everyday actions, from walking to driving, and are essential for mechanical operations.

acceleration and force

Acceleration and force are deeply interconnected concepts in physics, with their relationship being outlined in Newton's second law. Acceleration is the rate at which an object changes its velocity. When a force is applied to an object, it accelerates in the direction of that force.

In simple terms:

• The greater the force applied, the greater the acceleration, assuming mass is constant.
• Conversely, if the same force is applied to objects of varying mass, the object with less mass will accelerate more.

This interplay between force and acceleration is critical in problem-solving. In our example, we know the pulling force and the mass, and need to find the net force and frictional force, understanding that acceleration is given. Calculating these helps describe how objects begin to move, change direction, or stop.

This knowledge also finds application in everyday life, from starting a car to moving furniture. Recognizing how much force to apply for the desired acceleration can make tasks more efficient and effective.