Answer:
The change in gravitational potential energy is -1.80x10⁵ J.
Explanation:
The change in gravitational potential energy is given by:
Where:
"i" is for final and "f" for final
m: is the mass
g: is the gravity = 9.81 m/s²
h: is the height
For the car and the passengers we have:
The minus sign is because when the elevator car and the passengers are up they have a bigger gravitational potential energy than when they are in the ground.
Therefore, the change in gravitational potential energy is -1.80x10⁵ J.
I hope it helps you!
Answer:
Explanation:
Although there is absolutely NO regard for significant digits, I can help you with this, nonetheless.
The equation for Potential Energy is PE = mgh. We have everything but the height of the ball. We have to solve for that using a one-dimensional motion equation:
v² = v₀² + 2aΔx, where Δx is our displacement (the height we need for PE). Filling in and keeping in mind that at the max height of parabolic travel, the final velocity of the object is 0:
0 = (21.5)² + 2(-9.8)Δx and
0 = 462.25 - 19.6Δx and
-462.25 = -19.6Δx so
Δx = 23.58 m. Using this as the h in our PE equation:
PE = .19(9.8)(23.58) so
PE = 43.9 J, choice C.
It transfers energy through the source of the sound. Your ear detects sound waves when vibrating air particles cause your ear drum to vibrate
<span>K.E = 0.5 * m * v^2 ( m = mass(Kg), V = Velocity(m/s)
= 0.5 * 8 * 5^2
= 4 * 25
= 100 J </span>
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.
