Answer:
(for small oscillations)
Explanation:
The total energy of the pendulum is equal to:
For small oscillations, the equation can be re-arranged into the following form:
Where:
, measured in radians.
If the amplitude of pendulum oscillations is increase by a factor of 4, the angle of oscillation is 
and the total energy of the pendulum is:
The factor of change is:
Answer:
Explanation:
Given:
- charge on the alpha particle,
- mass of the alpha particle,
- strength of a uniform magnetic field,
- radius of the final orbit,
<u>During the motion of a charge the magnetic force and the centripetal forces are balanced:</u>
where:
v = velocity of the alpha particle
Here we observe that the velocity of the aprticle is close to the velocity of light. So the kinetic energy will be relativistic.
<u>We firstly find the relativistic mass as:</u>
now kinetic energy:
Answer:
Correct sentence: gravitational potential energy of the mass on the hook.
Explanation:
The mechanical energy of a body or a physical system is the sum of its kinetic energy and potential energy. It is a scalar magnitude related to the movement of bodies and to forces of mechanical origin, such as gravitational force and elastic force, whose main exponent is Hooke's Law. Both are conservative forces. The mechanical energy associated with the movement of a body is kinetic energy, which depends on its mass and speed. On the other hand, the mechanical energy of potential origin or potential energy, has its origin in the conservative forces, comes from the work done by them and depends on their mass and position. The principle of conservation of energy relates both energies and expresses that the sum of both energies, the potential energy and the kinetic energy of a body or a physical system, remains constant. This sum is known as the mechanical energy of the body or physical system.
Therefore, the kinetic energy of the block comes from the transformation in this of the gravitational potential energy of the suspended mass as it loses height with respect to the earth, keeping the mechanical energy of the system constant.
