**Solution**From Figure 8.12, the forces causing torques are the wall force \(\vec{R}\), the gravity forces on the beam and the man, \(w_B\) and \(w_M\), and the tension force \(\vec{T}\). Apply the condition of rotational equilibrium.Compute torques around the pin at \(O\), so \(\tau_R = 0\) (zero moment arm). The torque due to the beam’s weight acts at the beam’s center of gravity.Substitute \(L = 5.00 \, \text{m}\) and the weights, solving for \(T\).\[\sum \tau_i = \tau_R + \tau_B + \tau_M + \tau_T = 0\]\[\sum \tau_i = 0 - w_B(L/2) - w_M(1.50 \, \text{m}) + TL \sin(53.0^\circ) = 0\]\[-(3.00 \times 10^2 \, \text{N})(2.5 \, \text{m}) - (6.00 \times 10^2 \, \text{N})(1.50 \, \text{m}) + (T \sin 53.0^\circ)(5.00 \, \text{m}) = 0\]\[ T = \underline{\hspace{2cm}} \, \text{N} \]Now apply the first condition of equilibrium to the beam.Substituting the value of \(T\) found in the previous step and the weights, obtain the components of \(\vec{R}\).\[\sum F_X = R_X + T \cos 53.0^\circ = 0 \quad (2)\]\[\sum F_Y = R_Y - w_B - w_M + T \sin 53.0^\circ = 0 \quad (2)\]\[ R_X = \underline{\hspace{2cm}} \, \text{N} \]\[ R_Y = \underline{\hspace{2cm}} \, \text{N} \]---**Remarks** Even if we selected some other axis for the torque equation, the solution would be the same. For example, if the axis were to pass **Example 8.7 Walking a Horizontal Beam****Goal** Solve an equilibrium problem with nonperpendicular torques.**Problem** A uniform horizontal beam 5.00 m long and weighing 3.00 × 10² N is attached to a wall by a pin connection that allows the beam to rotate. Its far end is supported by a cable that makes an angle of 53.0° with the horizontal (Fig. 8.12a). If a person weighing 6.00 × 10² N stands 1.50 m from the wall, find the magnitude of the tension \(\vec{T}\) in the cable and the force \(\vec{R}\) exerted by the wall on the beam.**Figure 8.12**- **(a)** A uniform beam attached to a wall and supported by a cable.- **(b)** A free-body diagram for the beam.- **(c)** The component of the free-body diagram.**Diagrams Explanation**- **(a)** Illustrates a side view of the setup, showing the beam attached to the wall with a cable making a 53.0° angle. A person stands on the beam, 1.50 m away from the wall.- **(b)** Displays the forces acting on the beam: the person's weight (600 N), the beam's weight (300 N), and the tension (\(\vec{T}\)) and reaction force (\(\vec{R}\)) vectors.- **(c)** Breaks down the forces into components based on the angle: \(T \sin 53.0°\) and \(T \cos 53.0°\). Reaction forces from the wall are labeled as \(R_x\) and \(R_y\).**Strategy** The second condition of equilibrium, \(\Sigma \tau_i = 0\), with torques computed around the pin, can be solved for the tension \(T\) in the cable. The first condition of equilibrium, \(\Sigma \vec{F}_i = 0\), gives two equations and two unknowns for the two components of the force exerted by the wall, \(R_x\) and \(R_y\).

Answered: Image /qna-images/answer/1530af70-f11e-406a-b23e-cae973905cbc.jpg

Problem A uniform horizontal beam 5.00 m long and weighting 3.00 × 102 N is attached to a wall by a pin connection that allows the beam to rotate. Its far end is supported by a cable that makes an angle of 53.0° with the horizontal (Fig. 8.12a). If a person weighing 6.00 × 102 N stands 1.50 m from the wall, find the magnitude of the tension T in the cable and the force R exerted by the wall on the beam. R 53.0 300 N 600 N (b) R, T sin 53.0° R T cos 53.0° 53.0% 4.50 m→ 300 N 2.50 m- 600 N 5.00 m (a) (c)

Problem A uniform horizontal beam 5.00 m long and weighting 3.00 × 102 N is attached to a wall by a pin connection that allows the beam to rotate. Its far end is supported by a cable that makes an angle of 53.0° with the horizontal (Fig. 8.12a). If a person weighing 6.00 × 102 N stands 1.50 m from the wall, find the magnitude of the tension T in the cable and the force R exerted by the wall on the beam. R 53.0 300 N 600 N (b) R, T sin 53.0° R T cos 53.0° 53.0% 4.50 m→ 300 N 2.50 m- 600 N 5.00 m (a) (c)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A 1140-N uniform beam is attached to a vertical wall at one end and is supported by a cable at the other end. A 1960-N crate hangs from the far end of the beam. Using the data shown in the figure, find (a) the magnitude of the tension in the wire and the magnitudes of the (b) horizontal and (c) vertical components of the force that the wall exerts on the left end of the beam. 50.0° 30.0% Beam 1960 N
(a) A man stands a distance d = 0.250 m from the left end of a board as shown in the figure. The board is supported by three cords. Find the tension in each cord (in N). Assume the board is uniform, with length L = 2.00 m and mass 32.5 kg, and the weight of the man is 690 N. (Due to the nature of this problem, do not use rounded intermediate values-including answers submitted in WebAssign-in your calculations.) 子。
A uniform bar with a length of 6.88 meters and a mass of 29 kg is attached to a building by an axis at its left end. A box of mass 38.4 kg sits on the bar at a distance of 2.4 m from the left end. The right end of the bar is supported by a cable with a 477.81 N of tension that is also attached to the building. The angle between the cable and the bar is 34.9°. Determine the Fv, the vertical force on the bar by the wall (in N).
A worker of weight 772.7 kg stands on the end of a beam of weight 1693 N and length L= 119.7 m, supported on a pivot. The beam's center of mass is at its center. W is the weight of a counterweight needed to hold the beam in equilibrium. Determine the counterweight W (in N) if the distance between the counterweight and the fulcrum is x= 27.5 m. Answer:
6m T 10m A 8m Figure 4 A B 6. A horizontal beam AB of mass m = 20kg is supported from end B by a cable and hinged to a A vertical wall at end A. Calculate the magnitude of the tension T in the cable when Batman, who has a mass M = 80 kg, stands midway along the beam. What are the x and y components of the force at the hinge?
In the figure, one end of a uniform beam of weight 280 N is hinged to a wall; the other end is supported by a wire that makes angles θ = 28° with both wall and beam. Find (a) the tension in the wire and the (b) horizontal and (c) vertical components of the force of the hinge on the beam.
A shelf bracket is mounted on a vertical wall by a single screw. S S2 S1 Neglecting the weight of the bracket, and if s = 6.4 cm, s1 the horizontal force component exerted on the bracket by the screw when a 95.2 N vertical force is applied as shown. Imagine that the bracket is slightly loose. 5.4 cm and s2 = 2.2 cm, find =
(a) A student stands a distance d = 0.750 m from the left end of a beam as shown in the figure. The beam is supported by three lines. Find the tension in each line (in N). Assume the beam is uniform, with length L = 2.00 m and mass 29.5 kg, and the weight of the student is 725 N. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) 1731 = T₂ T₁ L -2.00 m
A scaffold of mass 79 kg and length 5.0 m is supported in a horizontal position by a vertical cable at each end. A window washer of mass 84 kg stands at a point 1.1 m from one end. What is the tension in (a) the nearer (relative to the person) cable and (b) the farther (relative to the person) cable? (a) Number i Units (b) Number i Units
The figure below shows a beam of uniform density with a mass of 35.5 kg and a length t5.95 m. It is suspended from a cable at a distance d 1.20 m from its left end, while its right end is supported by a vertical column. (a) What is the tension (in N) in the cable? (b) What is the magnitude of the force (in N) that the column exerts on the right end of the beam? Need Help? Read Page 20
In a city park a nonuniform wooden beam 4.00 m long is suspended horizontally by a light steel cable at each end. The cable at the left-hand end makes an angle of 30.0° with the vertical and has tension 620 N. The cable at the right-hand end of the beam makes an angle of 50.0° with the vertical. As an employee of the Parks and Recreation Department, you are asked to find the weight of the beam and the location of its center of gravity.
A plank which weighs 2.00 × 10- N with a length of 8.00 m is connected to a wall as seen in the figure below. The one end of the plank is held horizontally by a rope that makes an angle 1S of 53.0° with the plank. A man stands 2.00 m from the wall. Calculate the tension in the rope as well as the magnitude and direction of the force applied by the wall on the plank, if the man weighs 6.00 x 102-N. I 8.00 m