Work And Energy

Step 1: Definition of Conservative Force.
A force is called conservative if the work it does on an object depends only on the initial and final positions of the object and not on the path taken. In other words, the work done by a conservative force in moving an object between two points is the same regardless of the path followed. Some examples of conservative forces are gravitational force and spring force.
Step 2: Analyze each statement.
(1) The work done by the conservative force depends only on the end points. This is true. For a conservative force, the work done is independent of the path taken and depends only on the initial and final positions of the object.
(2) The work done by a conservative force in a closed path is zero. This is true. If a conservative force acts on an object and the object returns to its original position (closed path), the net work done by the force is zero because the work depends only on the initial and final positions, which are the same in a closed path.
(3) Spring force and frictional force are conservative. This is NOT true. The spring force is a conservative force (it follows Hooke's law), but frictional force is non-conservative. Friction depends on the path taken and dissipates energy, converting mechanical energy into heat.
(4) The total mechanical energy of a system is conserved if forces doing work are conservative. This is true. If only conservative forces are acting, the total mechanical energy (kinetic + potential) of the system is conserved. Non-conservative forces, like friction, dissipate energy, so mechanical energy is not conserved.
Step 3: Conclusion.
The statement that is NOT true for a conservative force is statement (3), as friction is a non-conservative force, not a conservative one.

Step 1: Using the work-energy principle.
The work done by the force exerted on the block is equal to the change in the kinetic energy of the bullet. The bullet is initially moving at 50 m/s, and after penetrating 20 cm into the block, it comes to rest. Therefore, the initial kinetic energy of the bullet is converted into work done in stopping the bullet. The kinetic energy of the bullet is given by: where:
(mass of the bullet),
(velocity of the bullet).
Substitute the values: Step 2: Calculating the force.
The work done by the force in bringing the bullet to rest is equal to the force multiplied by the distance over which the bullet penetrates the block, i.e., 20 cm = 0.2 m. The work done is: where:
(distance the bullet penetrates the block),
(work done).
Since work done is equal to kinetic energy, we have: Solve for : Step 3: Conclusion.
Thus, the magnitude of the force exerted on the wooden block is .