Correct A traffic light hangs from a pole as shown in (Figure 1) The uniform alu
ID: 1444799 • Letter: C
Question
Correct A traffic light hangs from a pole as shown in (Figure 1) The uniform aluminum pole AB is 8.00 m long and has a mass of 13.0 kg. The mass of the traffic light is 20.5 kg Significant Figures Feedback: Your answer 328.3 N was either rounded differently or used a different number of significant figures than required for this part Figure 1 of 1 Part C Determine the horizontal component of the force exerted by the pivot A on the aluminum pole. Express your answer to two significant figures and include the appropriate units. Enter positive value if the direction of the force is to the right and negative value if the direction of the force is to the left. 37° 3.80 m FAzVale Units Submit My Answers Give UpExplanation / Answer
The tension from the cable is not acting at the tip of the pole, but only partially up the pole and before the hanging stop light. The distance that the cable connects to the hanging pole is the hypotenuese of a triangle which has a side of 3.8 m and opposite angle of 37 degrees, so the length of this hypotenuse is
L*sin(37) = 3.80m =====> L = 6.3 m
If we start by considering Newton’s 2nd Law for angular rotation, and take our rotation through the base A, then we get
A) Sum() = T sin(37)(6.3m) (20.5kg)(g) (cos53)(8.0m) (13.0kg)(g) (cos53)(8.0/2) = 0
We show the force of the weight of the pole acting from its center of mass (middle) since it is uniform.
On solving, T = 336 N
B) and C) Next we sum the forces in the x y directions, and since the system is static, these sums are zero, in which case: Sum(Fx) = F1 - T = 0 ==========> F1 = T = 336 N
Sum(Fy) = F2 Mg mg = 0 ======> F2 = (M + m)g = 328.3 N