Answer:
A) 12.57 m
B) 5 RPM
C) 3.142 m/s
Explanation:
A) Distance covered in 1 Revolution:
The formula that gives the relationship between the arc length or distance covered during circular motion to the angle subtended or the revolutions, is given as follows:
s = rθ
where,
s = distance covered = ?
r = radius of circle = 2 m
θ = Angle = 2π radians (For 1 complete Revolution)
Therefore,
s = (2 m)(2π radians)
<u>s = 12.57 m</u>
B) Angular Speed:
The formula for angular speed is given as:
ω = θ/t
where,
ω = angular speed = ?
θ = angular distance covered = 15 revolutions
t = time taken = 3 min
Therefore,
ω = 15 rev/3 min
<u>ω = 5 RPM</u>
C) Linear Speed:
The formula that gives the the linear speed of an object moving in a circular path is given as:
v = rω
where,
v = linear speed = ?
r = radius = 2 m
ω = Angular Speed in rad/s = (15 rev/min)(2π rad/1 rev)(1 min/60 s) = 1.571 rad/s
Therefore,
v = (2 m)(1.571 rad/s)
<u>v = 3.142 m/s</u>
Answer:
Explanation:
Part 0
All the spring moves is 2 cm
x = 2 cm * [1 m / 100 cm ]
x = 0.020 meters
F = k*d
100N = k * 0.02 m
100 N / 0.02 = k
5000 N / m
Part A
The spring feels a force of 100 N - - 100N = 200 N because each person is pulling in the opposite direction.
F = k * x
200N = 5000 N/m * d
200 / 5000 = d
d = 0.04 meters.
Part B
10.2 kg must be converted to a force as experienced here on earth.
F = m * g
g = 9.81
m = 10.2
F = 10.2 * 9.81
F = 100.06 N
F = k * d
100.06 = 5000 * d
d = 100.06 / 5000
d = 0.02 meters.
Answer:
The speed after being pulled is 2.4123m/s
Explanation:
The work realize by the tension and the friction is equal to the change in the kinetic energy, so:
(1)
Where:
Because the work made by any force is equal to the multiplication of the force, the displacement and the cosine of the angle between them.
Additionally, the kinetic energy is equal to 
, so if the initial velocity 
is equal to zero, the initial kinetic energy 
is equal to zero.
Then, replacing the values on the equation and solving for 
, we get:
So, the speed after being pulled 3.2m is 2.4123 m/s
Answer: 0K
Explanation:
Absolute 0 (0K) is the point where nothing could be colder and no heat energy remains in a substance.
Answer:
The gravitational force between m₁ and m₂, is approximately 1.06789 × 10⁻⁶ N
Explanation:
The details of the given masses having gravitational attractive force between them are;
m₁ = 20 kg, r₁ = 10 cm = 0.1 m, m₂ = 50 kg, and r₂ = 15 cm = 0.15 m
The gravitational force between m₁ and m₂ is given by Newton's Law of gravitation as follows;
Where;
F = The gravitational force between m₁ and m₂
G = The universal gravitational constant = 6.67430 × 10⁻¹¹ N·m²/kg²
r₂ = 0.1 m + 0.15 m = 0.25 m
Therefore, we have;
The gravitational force between m₁ and m₂, F ≈ 1.06789 × 10⁻⁶ N
