Work Energy And Power

Step 1: Understanding the Question:
The question describes a cyclist moving up a hill without pedaling, and we must consider the situation under the assumption of "no loss of energy" (i.e., no friction or air resistance). We need to determine what happens to the cyclist's energy.
Step 2: Key Formula or Approach:
The Principle of Conservation of Mechanical Energy states that if there are no non-conservative forces (like friction or air resistance) doing work, the total mechanical energy of a system remains constant.
Total Mechanical Energy (TME) = Kinetic Energy (KE) + Potential Energy (PE).
Step 3: Detailed Explanation:
The problem explicitly states to assume "no loss of energy". This means we can apply the Principle of Conservation of Mechanical Energy.
As the cyclist moves up the hilly track, his height (h) above the starting point increases.
- Because height (h) increases, his potential energy ( ) increases.
- Since the total mechanical energy ( ) must remain constant, and PE is increasing, his kinetic energy ( ) must decrease. This means his speed (v) decreases.
- Let's analyze the options:
(A) his kinetic energy remains constant: Incorrect. It decreases as he goes up.
(B) his potential energy remains constant: Incorrect. It increases as he goes up.
(C) his total mechanical energy continuously increases: Incorrect. It is conserved (remains constant).
(D) his total mechanical energy remains constant: Correct. This is the direct consequence of the conservation of energy principle.
Step 4: Final Answer:
According to the law of conservation of energy, with no energy loss, the total mechanical energy of the cyclist remains constant. The energy transforms from kinetic to potential energy as he moves uphill.

Step 1: Understanding Work Done:
Work done ( ) by a force depends on the force applied and the displacement of the object along the direction of the force. - If the force vector is constant and the displacement is , then work done is , where is the angle between the force and displacement vectors. - If the force is applied along a path, the work done is the integral of the force component along the path, .
Step 2: Calculating Work Done for Each Case:
The net displacement from A to B is a straight line of length m.
Case 1: The force F is applied tangentially along the semi-circular path AJB. The length of the path is the circumference of the semi-circle, . The radius is m. So, path length m. Since the force is always in the direction of motion, the work done is force distance. Case 2: The constant force F is applied horizontally, parallel to the displacement AB. The displacement is m. The angle between force and displacement is . Case 3: The constant force F is applied at an angle to the horizontal displacement AB. The displacement is m. The angle between force and displacement is . Given that , we know that . Therefore, is less than . For example, if , .
Step 3: Comparing the Work Done:
We have: - - - , which is less than . Comparing the three values, we get: .
The ascending order is Case 3, Case 2, Case 1.

Step 1: List the given data and convert units:
- Mass ( ) = 20 g = 0.02 kg - Initial height ( ) = 45 m - Rebound height ( ) = 40 m - Acceleration due to gravity ( ) = 10 m/s
(a) Initial Potential Energy:
The potential energy (PE) of an object is given by the formula . (b) Speed on hitting the ground:
By the principle of conservation of energy (assuming no air resistance), the initial potential energy is completely converted into kinetic energy (KE) just before the ball hits the ground. (c) Loss in kinetic energy:
The loss in kinetic energy during the collision is the difference between the kinetic energy just before hitting the ground and the kinetic energy just after rebounding. - Kinetic energy just before impact: J. - The kinetic energy just after rebound is equal to the potential energy it gains on reaching the rebound height . - The loss in kinetic energy is:

Step 1: Understanding the Scale:
The subatomic scale refers to particles smaller than an atom, like electrons, protons, and neutrons. The energies and work done involved at this level are extremely small compared to macroscopic standards.
Step 2: Defining the Unit:
The standard SI unit for work and energy is the Joule (J). However, the Joule is too large for convenient use on the subatomic scale. A more practical unit is the electron-volt (eV).
One electron-volt is defined as the amount of kinetic energy gained (or work done) by a single electron when it is accelerated through an electric potential difference of one volt.
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