Answer:
b. -11.6 cm
Explanation:
We have given parameters:
Length, l = 1.5 m = 150 cm
Mass of weight, 
= 20 kg
Width, x = 4 cm
Distance d = 4 cm
Mass of bar, 
= 5 kg
We are asked to find the center of mass from the mid-point, 
Since 3 weights are on the left and 2 weights are on the right, we know:
= 3 * 20 = 60 kg
= 2 * 20 = 40 kg
And also we know that, 
= 150/2 = 75 cm
For the left side, center of mass is:
cm
From the midpoint, the distance to the left is:
cm
For the right side, center of mass is:
cm
From the midpoint, the distance to the right will be:
cm
Hence,
cm
Answer:
Substance X will rise due to convection.
Explanation:
Answer:
W = 311074.5 [J]
Explanation:
In order to solve this problem we must analyze two parts, in the first part by means of Newton's second law we can determine the acceleration of the beam, remembering that the sum of the forces is equal to the product of mass by acceleration.
∑F = m*a
F = forces acting on the beam [N]
m = mass = 425 [kg]
a = acceleration = 1.8 [m/s²]
The forces acting on the beam are the force of the crane up (positive) and the weight of the beam down (negative)
![F_{crane}-(425*9.81)= 425*1.8\\F_{crane}=4713.25 [N]](https://tex.z-dn.net/?f=F_%7Bcrane%7D-%28425%2A9.81%29%3D%20425%2A1.8%5C%5CF_%7Bcrane%7D%3D4713.25%20%5BN%5D)
Now in the second part, we use the definition of work, which is equal to the product of the force applied in the direction of displacement, that is, the product of force by distance.
where:
W = work [J]
F = force = 4713.25 [N]
d = distance = 66 [m]
![W=4713.25*66\\W=311074.5[J]](https://tex.z-dn.net/?f=W%3D4713.25%2A66%5C%5CW%3D311074.5%5BJ%5D)
Answer:
a) x₀ = - 2 m , b) y = 4.47 m
Explanation:
A wave travels in the middle with constant speed, let's use the equation of uniform motion
v = d / t
t = d / v
The distance to the first listeners, see attached
d₁ = x₀-x
t = (x₀ +7) / v
The distance to the second listener
d₂ = x - x₀
t = (+ 3- x₀) / v
As the wave arrives at the same time, we can equal the two equations
(x₀ +7) / v = (3 -x₀) / v
x₀ + 7 = 3 - x₀
2 x₀ = 3 - 7
x₀ = -4/2
x₀ = - 2 m
b) The time it takes for the wave to reach the listeners of the x-axis, where the speed of sound is 340 m / s
t = 5/340
t = 0.0147 s
Let's look for the distance the wave travels for the listener axis and
v = d₃ / t
d₃ = v.t
d₃ = 340 * 0.0147
d₃ = 5 m
For the distance component we use the Pythagorean triangle
d₃² = x₀² + y²
y² = d₃² - x₀²
y = √ (d₃² -4)
y = √ (5² -4)
y = 4.47 m
Explanation:
It is given that,
Frequency of vibration, f = 215 Hz
Amplitude, A = 0.832 mm
(a) Let T is the period of this motion. It is given by the following relation as :
(b) Speed of sound in air, v = 343 m/s
It can be given by :
Hence, this is the required solution.
