Q8 Please explain this question`s answerA small body slides from rest............

To address the question about a small body sliding from rest, we first need to understand the context and the principles involved. Typically, this scenario involves concepts from physics, particularly those related to motion, forces, and energy. Let’s break it down step by step.

Understanding the Scenario

Imagine a small object, like a block, positioned at the top of a frictionless incline. When released, it begins to slide down due to the force of gravity. The key points to consider here are:

• The object starts from rest, meaning its initial velocity is zero.
• The only force acting on it is gravity, which pulls it down the slope.
• We can ignore air resistance and friction for simplicity.

Applying Newton's Laws

According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In this case, the net force is the component of gravitational force acting down the slope.

The gravitational force can be calculated using the formula:

F = m * g

Where:

• F is the force due to gravity.
• m is the mass of the object.
• g is the acceleration due to gravity (approximately 9.81 m/s² on Earth).

Calculating Acceleration

To find the acceleration of the block down the incline, we need to consider the angle of the slope (let’s call it θ). The component of gravitational force acting down the slope can be expressed as:

F_parallel = m * g * sin(θ)

Using Newton's second law, we can set up the equation:

m * a = m * g * sin(θ)

Here, the mass (m) cancels out, leading us to:

a = g * sin(θ)

Velocity and Distance Traveled

Now that we have the acceleration, we can determine how fast the block will be moving after sliding down a certain distance. Since the block starts from rest, we can use the kinematic equation:

v² = u² + 2as

Where:

• v is the final velocity.
• u is the initial velocity (0 in this case).
• a is the acceleration we calculated.
• s is the distance traveled down the slope.

Substituting the values, we get:

v² = 0 + 2(g * sin(θ)) * s

This equation allows us to find the final velocity of the block after it has traveled a distance s down the incline.

Energy Considerations

Another way to analyze this situation is through the conservation of energy. The potential energy at the top of the incline converts into kinetic energy as the block slides down. The potential energy (PE) can be expressed as:

PE = m * g * h

Where h is the height of the incline. As the block descends, this potential energy transforms into kinetic energy (KE):

KE = 0.5 * m * v²

Setting the potential energy equal to the kinetic energy gives us:

m * g * h = 0.5 * m * v²

Again, the mass cancels out, leading to:

g * h = 0.5 * v²

This relationship can also help us find the final velocity, reinforcing the idea that energy is conserved in this system.

Conclusion

In summary, when a small body slides from rest down an incline, we can analyze its motion using Newton's laws, kinematic equations, and energy conservation principles. By understanding the forces at play and applying these concepts, we can predict the object's behavior as it moves down the slope. This approach not only enhances our grasp of physics but also illustrates the interconnectedness of different physical principles.