If a mass of .343 kg moves down a 5m ramp in 5.8 seconds, what is the velocity and KE developed by the moving mass
1 answer:
Velocity 0.86m/s
0.13J
Explanation:
Given parameters:
Mass = 0.343kg
distance = 5m
time taken = 5.8s
Unknown:
Velocity of mass = ?
Kinetic energy = ?
Solution:
Velocity is the rate of change of displacement with time. It is a vector quantity that shows magnitude and direction.
Mathematically;
Velocity =
Velocity = = 0.86m/s
Kinetic energy is the energy due to the motion of a body. It is expressed mathematically as:
Kinetic energy =
m is the mass
v is the velocity
Kinetic energy = = 0.13J
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1) The potential energy is the most at the highest position and the least at the equilibrium position
2) The kinetic energy is the most at the equilibrium position and the least at the highest position
Explanation:
1)
The potential energy of an object is the energy possessed by the object due to its position in a gravitational field; mathematically, it is given by
where
m is the mass of the object
g is the strength of the gravitational field
h is the height of the object relative to the ground
For the pendulum in this problem, m is the mass of the bob, and h is the height of the above relative to the ground. We see from the formula that the potential energy is directly proportional to the height:
This means that:
- The potential energy is the most when the bob is at the highest position
- The potential energy is the least when the bob is at the equilibrium position, which is the lowest position
2)
We can solve this part by applying the law of conservation of energy: in fact, the total mechanical energy of the pendulum (sum of potential and kinetic energy) is constant at any time during the motion,
where KE is the kinetic energy.
From the equation above, we observe that:
- When PE is maximum, KE must be at minimum
- When PE is minimum, KE must be maximum
Therefore, this implies that:
- The kinetic energy is the most when the potential energy is the least, i.e. at the equilibrium position
- The kinetic energy is the least when the potential energy is the most, i.e. at the highest position
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