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.
Answer:
a. A baseball after it has been hit - not in free fall
b. A rock that is thrown in the air - not in free fall
c. The moon - free-fall
d. A paper airplane - not in free fall
e. A bird flying - not in free fall
Explanation:
- The free-fall is defined as the falling of an object due to the action of gravity. The object is not experiencing any other force neglecting the air resistance.
- If an object is in free-fall, the direction of its motion is directed towards the center of the earth. It does not have a horizontal component of velocity.
- If the body is under free-fall, but a centripetal force acts on it where it is equal to the gravitational force at that point. The object will have two components of velocity along the tangential line, perpendicular to the radius of the orbit.
a. A baseball after it has been hit - not in free fall according to point 1 & 2.
b. A rock that is thrown in the air - not in free fall according to point 1.
c. The moon - free-fall according to point 3.
d. A paper airplane - not in free fall according to point 1 & 2.
e. A bird flying - not in free fall according to point 1 & 2.
Answer: Yes.
Explanation:
Assuming Earth and Moon are isolated is space, it is possible to have a point where Earth and Moon will pull at an object with equal force.
That point will be closer to the Moon than the Earth because Moon's gravitational field strength is weaker than Earth's gravitational field strength.
Answer: the water level would rise since the pebble displaces minimal water compared to the boat.
Explanation:..........
