The diameter of the steel rod is 0.73 in.
What is the Modulus of elasticity?The modulus of elasticity, also known as Young's modulus, is a mechanical property that describes the stiffness of a material.
We know that;
E = F/A/e/l
E = F/A * l/e
E = Elasticity
F = force
A = Area
l = length
e = extension
As such we have that;
3 * 10^7 = 8 * 10^3/A * 35/0.022
3 * 10^7 =2.8 * 10^5/0.022A
A = 2.8 * 10^5/ 3 * 10^7 * 0.022
A = 2.8 * 10^5 /6.6 * 10^5
A = 0.42 ft^2
But;
A = πr^2
r =√ A/π
r =√ 0.42/3.14
r = 0.37 ft
D = 2r
= 0.73 in
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The air temperature in a 30 in.3 container with a free sliding piston is initially measured at 55 °F. The temperature is raised to 100 °F. What is the volume in the cylinder after the temperature has been raised?
A. 32.6 in^3
B. 54.5 in^3
C. 60 psi
D. 70 in^3
E. 16.5 in^3
Answer:
The answer is A. 32.6 in^3.
(Hope this helps)
Explanation:
Convert the initial and final temperatures from Fahrenheit to Kelvin. To do this, add 459.67 to each temperature.
Initial temperature = (55 + 459.67) K = 288.15 K
Final temperature = (100 + 459.67) K = 377.59 K
Plug in the given values into the ideal gas law equation: PV = nRT.
We are given that the volume of the container is 30 in^3, and the piston is free to move, so we can assume that the pressure is constant. We don't know the amount of gas (n), so we can leave that as a variable. The gas constant (R) is a known constant.
PV = nRT
30 P = n R 288.15
Rearrange the equation to solve for the volume at the final temperature.
PV = nRT
V = nRT/P
We want to solve for the new volume (V') at the final temperature, so we can substitute the new temperature (377.59 K) for T and solve for V':
V' = nR(377.59 K)/P
To find the value of n (the amount of gas), we can use the fact that the container has a constant pressure. This means that the product of pressure and volume is constant.
P1V1 = P2V2
Plugging in the initial values, we get:
P1V1 = P2V2
55 P = P2 V2
V2 = 55P/P2 * V1
where V1 is the initial volume (30 in^3).
Substituting this expression for V2 into the equation for V', we get:
V' = nR(377.59 K)/P = nR(377.59 K)/(55P/P2 * V1) = nR(377.59 K)/(55P/P2 * 30 in^3)
Simplify the expression by canceling out the P terms and plugging in the value for R:
V' = (n * 0.0821 Latm/molK * 377.59 K) / (55/P2 * 30 in^3)
V' = (n * 25.31) / (55/P2)
We can use the ideal gas law again to solve for n. At the initial conditions, we can solve for n as follows:
PV = nRT
30 P = n R 288.15 K
n = 30 P / (R * 288.15 K)
Substituting this expression for n into the equation for V', we get:
V' = [(30 P / (R * 288.15 K)) * 0.0821 Latm/molK * 377.59 K] / (55/P2 * 30 in^3)
Simplify the expression by canceling out units and plugging in the numerical values:
V' = (2.37 P2) in^3
So, the volume of the container at the final temperature is 2.37 P2 cubic inches. The answer is not one of the given options, but we can check that 2.37 P2 is closest to option (E), which is 16.5 in^3.
Please help me solve this.
The moment the ball leaves the tee, the velocity that is directed in the horizontal and the vertical directions is C) Horizontal = 22,98 ft/sec and Vertical = 19.28 ft/sec
How to explain the velocityThe golf ball is hit off a tee at a 40 degree angle from the ground. The golfer's swing causes the ball to leave the tee with an initial velocity of 30 ft/sec.
In this case, v initial = 30 ft/sec and theta = 40 degrees. So we have:
v(horizontal) = 30 * cos(40) ≈ 22.98 ft/sec
The correct option is C.
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Please help me solve this.
The moment of the wrench is
h -10 lb - ft How to find the moment of the wrenchThe Moment of Force, more commonly referred to as Torque, is a metric reflecting the magnitude of turning pressure or rotational force that a given force applies to an object about a certain point or axis.
The statement regarding the moment of a force is expressed through this formula:
Moment (or Torque) = Force × Perpendicular Distance
where
F = 20 lb
d = 2 in + 4 in = 6 in
d in ft = 6 / 12 = 0.5 ft
M = F x d
M = 20 lb * 0.5 ft
M = 10 lb - ft
for the direction given we have
M = -10 lb - ft
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Please help me solve this.
The mechanical advantage of the pulley system is 6
What is mechanical advantage?Mechanical advantage is the ratio of the load to the effort applied on a machine. It is also called force ratio. This is because both load and effort are forces. Mechanical advantage does not have unit.
Mechanical advantage can be expressed as;
MA = load/effort
In a pulley system, the number of pulley determines both the mechanical advantage and velocity ratio.
There are 6 pulleys in the load and one for effort
MA = load/effort
MA = 6/1 = 6
therefore the mechanical advantage of the pulley system is 6
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