the displacement (in centimeters) of a particle s moving back and forth along a straight line is given by the equation s
1 answer:
Answer:
In a simple harmonic motion, the displacement is given as .
Explanation:
- The motion described here could be just a periodic motion or a simple harmonic motion.
- If it is just a mere periodic motion it would have a different formula for the displacement but if it is a simple harmonic motion with the characteristic equation
, then its displacement measured from the equilibrium position or the centre could be written as
in which
represent the amplitude, angular velocity and the time respectively.
- The distances are measured in meters, time in seconds and angular velocity in radians per second in the SI system and since the final answer is requested in centimetres a conversion may be performed appropriately.
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Answer:
Both its temperature and its thermal energy will increase.
Explanation:
Objects are made up of particles. For example, water is made up of water molecules. The kinetic energy of a particle of mass and velocity
is equal to
,
- The thermal energy of an object measures the total kinetic energy of all its particles.
- On the other hand, the temperature of that object measures the average kinetic energy of all these particles.
Water in that pot gains energy when the pot is heated. That would increase the total kinetic energy of these water molecules.
What about temperature? Assume that the number of water particles in the pot stays the same- In other words, assume that water in the pot does not evaporate. As the total kinetic energy of these water molecules increase, their average kinetic energy would also increase. As a result, it would appear that the temperature of water in that pot has increased.
1) Mechanical energy is conserved in all the 4 situations
2) True
3) The potential energy of the block is 490 J
Explanation:
1)
Mechanical energy is the sum of potential energy (PE) and kinetic energy (KE) of a body:
According to the law of conservation of energy, in absence of non-conservative forces (such as air resistance, friction...), the mechanical energy of a body is always conserved.
This means that the mechanical energy is conserved in all the situations described. More specifically:
- Child on a swing : there is a continuous conversion between kinetic energy and gravitational potential energy
- Pendulum : there is a continuous conversion between kinetic energy and gravitational potential energy
Bow and Arrow : there is a conversion of energy from elastic potential (when the bow is stretched) to kinetic energy (when the arrow is shot)
Roller Coaster: there is a continuous conversion between kinetic energy and gravitational potential energy
2)
As we said, the mechanical energy of the object falling down at any point of the fall is
where KE is the kinetic energy and PE is the potential energy. The value of E is constant, since the mechanical energy is conserved.
The potential energy is given by
where m is the mass of the object, g is the acceleration of gravity, h is the height of the object above the ground.
As the object falls, its height decreases, and therefore, the potential energy PE also decreases. But we said that E must remain constant: therefore, if PE decreases, this means that KE increases, therefore as the object falls, the potential energy is converted into kinetic energy (in fact, the speed of the object increases). So the statement is true.
3)
The potential energy of an object is given by the equation
where
m is the mass of the object
is the acceleration of gravity
h is the height of the object relative to the ground
For the block in this problem, we have:
m = 10 kg
h = 5 m
Substituting, we find its potential energy:
Learn more about potential energy and kinetic energy:
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