A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mp = 6.2 kg and the sign has a mass of mg = 17.3 kg. The length of the beam is L = 2.55 m. The sign is attached at the very end of the beam, but the horizontal wire holding up the beam is attached 2/3 of the way to the end of the beam. The angle the wire makes with the beam is 0 = 34.2°.
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- Sir Lancelot rides slowly out of the castle at Camelot and onto the 12.0-m-long drawbridge that passes over the moat (Figure 1). Unbeknownst to him, his enemies have partially severed the vertical cable holding up the front end of the bridge so that it will break under a tension of 5.80 x 103 N. The bridge has mass 200 kg and its center of gravity is at its center. Lancelot, his lance, his armor, and his horse together have a combined mass of 600 kg. Part A Will the cable break before Lancelot reaches the end of the drawbridge? O yes O no Part B Figure 1 of 1 If so, how far from the castle end of the bridge will the center of gravity of the horse plus rider be when the cable breaks? Express your answer in meters. L = m 12.0 m-A 520-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 110-N rod as indicated in the figure below. The left end of the rod is supported by a hinge and the right end is supported by a thin cable making a 30.0° angle with the vertical. (Assume the cable is connected to the very end of the 6.00-m-long rod, and that there are 2.00 m separating the wall from the sign.) A rectangular sign hangs along the bottom of a rod connected to a hinge on a wall on its left. A cable with tension T at the right end of the rod connects to the wall above the hinge and makes a 30.0° angle with the vertical. The right end of the sign is at the right end of the rod.(a) Find the (magnitude of the) tension T in the cable. N (b) Find the horizontal and vertical components of the force exerted on the left end of the rod by the hinge. (Take up and to the right to be the positive directions. Indicate the direction with the sign of your answer.)The bones of the forearm (radius and ulna) are hinged to the humerus at the elbow. The biceps muscle connects to the bones of the forearm about 2.15 cm beyond the joint. Assume the forearm has a mass of 2.45 kg and a length of 0.465 m. When the humerus and the biceps are nearly vertical and the forearm is horizontal, if a person wishes to hold an object of mass 5.35 kg so that her forearm remains motionless, what is the force F exerted by the biceps muscle? F=?
- A rod is laying on top on two poles. The rod is uniform and has a length of 3.22 m. The left pole is at the left end of the rod and the right pole is a 0.41m (d-0.41m) from the right side of the rod. What is the ratio of the forces F/FR on the rod due to the two poles?A 400-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 120-N rod as indicated in the figure below. The left end of the rod is supported by a hinge and the right end is supported by a thin cable making a 30.0° angle with the vertical. (Assume the cable is connected to the very end of the 6.00-m-long rod, and that there are 2.00 m separating the wall from the sign.) (a) Find the (magnitude of the) tension T in the cable.=_______N (b) Find the horizontal and vertical components of the force exerted on the left end of the rod by the hinge. (Take up and to the right to be the positive directions. Indicate the direction with the sign of your answer.) HORIZONTAL COMPONENT= _________N VERTICAL COMPONENT= _________NProblem 2: A uniform beam of length L = 1.9 m and mass M = 49 kg has its lower end fixed to pivot at a point P on the floor, making an angle 0 = 15° as shown in the digram. A horizontal cable is attached at its upper end B to a point A on a wall. A box of the same mass M as the beam is suspended from a rope that is attached to the beam one-fourth L from its upper end. M M.
- Question 4. A rod is lying on the top of a table. One end of the rod is hinged to the table so that the rod can rotate freely on the table top. Two forces, both parallel to the table top, act on the rod at the same place. One force is directed perpendicular to the rod and has a magnitude of 31 N. The second force has a magnitude of 52 N and is directed at an angle with respect to the rod. If the sum of the torques due to the two forces is zero, what must be the angle? Ans: 36.59°In the figure below, the cg of the pole held by the pole vaulter is 2.54 m from the left hand, and the hands are 0.733 m apart. Assume the vaulting pole has a mass of 3.32 kg.) (a) calculate the force (in N) exerted by his right hand ( enter the magnitude.) (b) calculate the force (in N) exerted by his left hand. ( enter the magnitude) (c) If each hand supports half the weight of the pole in the figure below , show that the second condition for equilibrium (net τ = 0) is satisfied for a pivot other than the one located at the center of gravity of the pole. Explicitly show how you follow the steps in the Problem-Solving Strategy for static equilibrium described above. Figure C is the last diagramThe system in the figure is in equilibrium. A concrete block of mass 314 kg hangs from the end of the uniform strut of mass 50.6 kg. For angles φ = 34.9° and θ = 59.0°, find (a) the tension T in the cable and the (b) horizontal and (c) vertical components of the force on the strut from the hinge.
- The bones of the forearm (radius and ulna) are hinged to the humerus at the elbow. The biceps muscle connects to the bones of the forearm about 2.15 cm beyond the joint. Assume the forearm has a mass of 2.35 kg and a length of 0.445 m. When the humerus and the biceps are nearly vertical and the forearm is horizontal, if a person wishes to hold an object of mass 6.15 kg so that her forearm remains motionless, what is the force F exerted by the biceps muscle? 5 Humerus. F= Elbow. Biceps muscle Radius Ulna Hand NA horizontal, uniform beam with a mass of 33.5 kg and a length ℓ = 5.80 m is suspended from a rope at a distance d = 1.20 m from its left end, while its right end is supported by a vertical column. A beam with a length of ℓ is suspended from a rope and supported by a vertical column. The rope is attached at a point that is a distance d from the left end of the beam. The column is beneath the right end of the beam. (a) Calculate the tension (in N) in the rope. N (b) Calculate the magnitude of the force (in N) that the column exerts on the right end of the beam.A 400.0-N sign hangs from the end of a uniform strut. The strut is 4.0 m long and weighs 600.0 N. The strut is supported by a hinge at the wall and by a cable whose other end is tied to the wall at a point 3.0 m above the left end of the strut. (a) What is the y component of the tension in the rope? (b) What is the x component of the tension in the rope? (c) What is the magnitude of the tension in the rope? (a) y component of the tension: Ty = (b) x component of the tension: Tx = (c) What is the magnitude of the tension in the rope?