Please help I don't know how to answer these questions!
1 answer:
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
Learn more about kinetic and potential energy:
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Answer:
(a) the final velocity of the cart is 0.857 m/s
(b) the impulse experienced by the package is 21.43 kg.m/s
(c) the fraction of the initial energy lost is 0.71
Explanation:
Given;
mass of the package, m₁ = 10 kg
mass of the cart, m₂ = 25 kg
initial velocity of the package, u₁ = 3 m/s
initial velocity of the cart, u₂ = 0
let the final velocity of the cart = v
(a) Apply the principle of conservation of linear momentum to determine common final velocity for ineleastic collision;
m₁u₁ + m₂u₂ = v(m₁ + m₂)
10 x 3 + 25 x 0 = v(10 + 25)
30 = 35v
v = 30 / 35
v = 0.857 m/s
(b) the impulse experienced by the package;
The impulse = change in momentum of the package
J = ΔP = m₁v - m₁u₁
J = m₁(v - u₁)
J = 10(0.857 - 3)
J = -21.43 kg.m/s
the magnitude of the impulse experienced by the package = 21.43 kg.m/s
(c)
the initial kinetic energy of the package is calculated as;
the final kinetic energy of the package;
the fraction of the initial energy lost;