Kinetic energy: the energy of motion
Work: the change in kinetic energy
Power: the rate of work done
Explanation:
The kinetic energy of an object is the energy possessed by the object due to its motion. Mathematically, it is given by:
where
m is the mass of the object
v is its speed
The work done an object is the amount of energy transferred; according to the energy-work theorem, it is equal to the change in kinetic energy of an object:
where
is the final kinetic energy
is the initial kinetic energy
Finally, the power is the rate of work done per unit time. Mathematically, ti can be expressed as
where
W is the work done
t is the time elapsed
Learn more about kinetic energy, work and power:
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Electrons: negative charge
Protons: positive charge
Neutrons: negative charge
The atom would have to have more electrons than protons
Hope this helps :)
Linear momentum has to be conserved. It was zero before the thread eas burned ... when nothing was moving ... so the momentum of the masses moving in opposite directions has to add up to zero. ... Momentum = mass times speed. ... In one direction, you have 5 kg times 1/5 m/s= 1 kg-m/s. ... We need 1 kg-m/s in the other direction. ... 7 kg times speed = 1 kg-m/s. ... Can you finish it from here ?
<u>Answer:</u>
Work input = Work output * Work against friction is your answer so C
<u>Explanation:</u>
I hope this helps you :)
Answer:
0.191 s
Explanation:
The distance from the center of the cube to the upper corner is r = d/√2.
When the cube is rotated an angle θ, the spring is stretched a distance of r sin θ. The new vertical distance from the center to the corner is r cos θ.
Sum of the torques:
∑τ = Iα
Fr cos θ = Iα
(k r sin θ) r cos θ = Iα
kr² sin θ cos θ = Iα
k (d²/2) sin θ cos θ = Iα
For a cube rotating about its center, I = ⅙ md².
k (d²/2) sin θ cos θ = ⅙ md² α
3k sin θ cos θ = mα
3/2 k sin(2θ) = mα
For small values of θ, sin θ ≈ θ.
3/2 k (2θ) = mα
α = (3k/m) θ
d²θ/dt² = (3k/m) θ
For this differential equation, the coefficient is the square of the angular frequency, ω².
ω² = 3k/m
ω = √(3k/m)
The period is:
T = 2π / ω
T = 2π √(m/(3k))
Given m = 2.50 kg and k = 900 N/m:
T = 2π √(2.50 kg / (3 × 900 N/m))
T = 0.191 s
The period is 0.191 seconds.
