The weightless strut in the figure below is not attached to the wall; it is prevented from falling only by friction. (Let w = 360 N, L = 5.25 m and h = 3.25 m.)
(a) Find the magnitude of the force of friction between the wall and the strut.
Correct: Your answer is correct.
(b) Find the normal force exerted by the wall on the strut.
Incorrect: Your answer is incorrect.
(c) Find the minimum coefficient of static friction.
for part A) tan^-1(3.25/5.25)=31.76 degrees
T=360/2sin31.76= 342 N
V=w-Tsin31.76= 360-342sin31.76= 180 N
part B) H-Tcos31.76 = 0
H=Tcos31.37 = 342cose31.76 = 290.79 N but it says my answer is wrong.
Not sure why your answer is wrong when the question is not even complete.
Let's review the solution step by step:
(a) Find the magnitude of the force of friction between the wall and the strut.
You correctly found the tension in the strut using the given weight and the angle between the strut and the horizontal. The tension is given by T = w / (2sinθ), where θ is the angle.
T = 360 N / (2sin(31.76°))
T ≈ 342 N
To find the force of friction, we need to calculate the vertical component of the weight, which is given by V = w - Tsinθ.
V = 360 N - 342 N * sin(31.76°)
V ≈ 180 N
Therefore, the magnitude of the force of friction between the wall and the strut is approximately 180 N. This confirms that your answer is correct.
(b) Find the normal force exerted by the wall on the strut.
To find the normal force, we need to calculate the horizontal component of the tension, which is given by H = Tcosθ.
H = 342 N * cos(31.76°)
H ≈ 290.79 N
Therefore, the normal force exerted by the wall on the strut is approximately 290.79 N. However, you mentioned that your answer was marked incorrect. Please double-check your calculations to identify any possible errors.
(c) Find the minimum coefficient of static friction.
To find the minimum coefficient of static friction, we can use the equation:
μs = (Ff / N)
Since we have found the force of friction in part (a) and the normal force in part (b), we can plug these values into the equation to find the minimum coefficient of static friction.
μs = (180 N / 290.79 N)
μs ≈ 0.620
Therefore, the minimum coefficient of static friction is approximately 0.620.
Please make sure to double-check your calculations for part (b) in order to identify any mistakes and find the correct value for the normal force.
To find the magnitude of the force of friction between the wall and the strut, you can use the equation:
Frictional force = Normal force * Coefficient of static friction
In this case, the strut is prevented from falling only by friction, so the frictional force must be equal to the weight of the strut (360 N).
Let's assume the normal force exerted by the wall on the strut is N, and the coefficient of static friction is μ. The equation can be rewritten as:
μN = 360 N
To solve for the normal force, you can use the equation:
N = Weight - T sin(θ)
In this case, the weight of the strut is given as 360 N. T is the tension in the strut, and θ is the angle of the strut with respect to the vertical. In this case, θ can be found using the given values for L (5.25 m) and h (3.25 m) with the equation:
θ = tan^(-1)(h/L)
By substituting the given values into the equation, you can find the value of θ, which is approximately 31.76 degrees.
Next, you can find T using the equation:
T = weight / (2 * sin(θ))
By substituting the given values into the equation, you can find the value of T, which is approximately 342 N.
Now, you can calculate the normal force N as:
N = weight - T * sin(θ)
Substituting the values, you get:
N = 360 N - 342 N * sin(31.76 degrees)
Calculating the value gives:
N ≈ 290.79 N
So the normal force exerted by the wall on the strut is approximately 290.79 N.
It seems that your calculation for part B is correct. However, it's possible that there was a rounding error or a mistake in the system that graded your answer.