Answer:
The moment is -78.4 N-m (clockwise).
Explanation:
Given:
Mass of the object (m) = 20 kg
Distance of the object from the knee joint (d) = 0.4 m
Weight of leg is not considered.
Acceleration due to gravity (g) = 9.8 m/s²
Now, weight of the object is equal to the product of its mass and acceleration due to gravity. So,
Weight = Mass × Acceleration due to gravity
=
We know that, moment of a force about a point is defined as the product of force applied and the perpendicular distance between the point and the line of application of force.
Moment of the given weight about the knee joint is given as:
Moment about knee joint = Weight × Distance from knee joint to weight
Moment about knee joint = 196 × 0.4 = 78.4 Nm
Now, from the diagram below, we can observe that, the weight acts vertically down and thus the sense of rotation about the knee joint at point O is clockwise. So, moment is negative.
Therefore, the moment is -78.4 N-m (clockwise).
To develop this problem, it is necessary to apply the concepts related to Beat
The Beat is an acoustic phenomenon that is generated by two sine waves interfering with slightly different frequencies. The beat frequency is equal to the difference in the frequencies of the two original waves:
Our values are given as
For the particular case we have two possible frequencies:
Therefore the two possibles frequencies of the other players note are 437.9Hz and 442.1Hz
Answer:
The maximum radius the asteroid can have for her to be able to leave it entirely simply by jumping straight up is approximately 1782.45 meters
Explanation:
Whereby the height the astronaut can jump on Earth = 0.500 m, we have the following kinematic equation;
v² = u² - 2·g·h
Where;
v = The final velocity
u = The initial velocity
g = The acceleration due to gravity ≈ 9.8 m/s²
h = The height she jumps
At the maximum height, = 0.500 m, she jumps, v = 0, therefore, we have;
0² = u² - 2·g·
u² = 2 × 9.8 × 0.5 = 9.8
u = √9.8 ≈ 3.13
u = 3.13 m/s
Her initial jumping velocity ≈ 3.13 m/s
Escape velocity,
Where;
M = The mass of the asteroid
G = The Universal gravitational constant = 6.67408 × 10⁻¹¹ m³/(kg·s²)
r = The radius of the asteroid
The average density of the Earth = 5515 kg/m³
The mass of the asteroid, M = Density × Volume = 5515 kg/m³× 4/3 × π × r³
The escape velocity, she has, ≈ 3.13 m/s is therefore;
Therefore, the maximum radius of the asteroid can have for her jumping velocity to be equal to the escape velocity for her to be able to leave it entirely simply by jumping straight up = r ≈ 1782.45 meters.