Problem:

A force F equal to 20 Newton is applied to a block at rest. After the block has moved a distance of 8 meters to the right, the direction of the horizontal component of the force F is reversed. Find the velocity with which the block arrives at its starting point.

Solution:

To solve this problem, we need to analyze the forces acting on the block and apply Newton's laws of motion.

1. Initial Analysis:

Before the direction of the horizontal component of the force is reversed, the block experiences a constant force of 20 Newton to the right. We assume that there are no other external forces acting on the block.

2. Applying Newton's Second Law:

Newton's second law states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. In equation form, it can be written as:

F = ma

Where F is the net force, m is the mass of the block, and a is the acceleration.

3. Calculating the Acceleration:

Since the block is initially at rest, we can assume its initial velocity (u) is zero. Therefore, the equation for calculating the final velocity (v) can be written as:

v^2 = u^2 + 2as

Where v is the final velocity, s is the displacement, and a is the acceleration.

Given that the block moves a distance of 8 meters, the equation becomes:

v^2 = 0 + 2a(8)
v^2 = 16a

4. Reversing the Direction of the Force:

When the direction of the horizontal component of the force is reversed, the block experiences a constant force of 20 Newton to the left. This means that the net force acting on the block is now the difference between the two forces:

Net Force = 20N - 20N = 0N

Since the net force is zero, the block experiences no acceleration. This means that the block will continue to move with a constant velocity.

5. Calculating the Final Velocity:

Since the block continues to move with a constant velocity, the final velocity is the same as the initial velocity. Therefore, we can conclude that the velocity with which the block arrives at its starting point is zero.

Conclusion:

The block arrives at its starting point with a velocity of zero. This is because the net force acting on the block becomes zero after the direction of the horizontal component of the force is reversed. Therefore, the block continues to move with a constant velocity until it reaches its starting point.