Statics Worksheet Solutions

1. A simple beam bridge is 50. 0 m long and has a mass of 20 1. A simple beam bridge is 50.0 m long and has a mass of 20.0 metric tons. (a) Find the center of mass of the bridge. (b) If the bridge is supported by a pillar at each end, find the force that each pillar exerts in supporting the bridge. (Hint: 1 metric ton = 1000 kg. Finding the torque about each pillar gives only one unknown for each equation.) mg F1 F2 Center of mass at the center of the beam, x = 25.0 m from left. From symmetry of forces F1 and F2 about the center, get F1 = F2. Use torque and a pivot point at the left end to get F1:

2. If a 5. 00 metric ton truck sits 20 2. If a 5.00 metric ton truck sits 20.0 m from the left end of the bridge, find the center of mass and the force of support from each pillar. 20.0 m mg bridge F1 F2 mg truck

2. {continued} Put pivot at left end to get the force F2 from torque: Use net force to get to F1:

3. Repeat #2 if a 7. 50 metric ton truck sits 10 3. Repeat #2 if a 7.50 metric ton truck sits 10.0 m from the right end of the bridge in addition to the 5.00 metric ton truck 20.0 m from the left. 20.0 m 10.0 m mg bridge F1 F2 mg truck mg other truck

3. {continued} Put pivot at left end to get the force F2 from torque: Use net force to get to F1:

4. A 20.0 kg sign is supported from the end of a massless horizontal 2.00 m rod. Find the tension in the rope and the force that the wall exerts on the beam. The rope is attached to the far end of the beam and makes an angle of 20.0 degrees to the horizontal. (You will have to use both SF = 0 and St = 0) T = force of tension Fy Fx q = 20.0o Put pivot at left end to get the tension force T from torque: mg sign

4. {continued} Use net force to get to Fx and Fy:

5. If the 2. 00 m rod in #4 has a mass of 8 5. If the 2.00 m rod in #4 has a mass of 8.50 kg and a uniform density, find the tension in the rope and the force that the wall exerts. T = force of tension Fy Fx q = 20.0o mg beam mg sign Put pivot at left end to get the tension force T from torque:

5. {continued} Use net force to get to Fx and Fy:

6. A steel beam of mass 1000 kg and length L is supported by posts at each end. A second beam, of equal density but half its length, lies in top of the first beam. If the left end of the top beam lines up with the left end of the left end of the bottom beam, find the force of support in each post. F1 F2

6. {continued} Put pivot at left end to get the force F2 from torque: Use net force to get to F1:

7. A 3.00 m beam extends horizontally from a wall and has a mass of 45.0 kg. A wire extends form the wall above the beam at an angle of 45.0 degrees and connects 1.00 meter from the end of the beam. Find the tension in the rope and the force that the wall exerts on the end of the beam. T = force of tension Fy Fx

7. {continued} Put pivot at left end to get the force F2 from torque: Use net force to get to Fx and Fy:

n = normal force by the wall 8. (a) A 5.00 m long ladder leans against a wall at a point 4.00 m above the ground. The ladder is uniform and has a mass of 12.0 kg. Assuming that the wall is frictionless (the ground is not frictionless), determine the forces exerted on the ladder by the ground and wall. {126 N @ 70o and 44 N} (b) A 60.0 kg painter stands on the ladder 3.00 meters along the ladder from the bottom. Find the force exerted on the ladder by the wall and the floor. (c) If the ladder just begins to slip at its base at this point, what is the coefficient of static friction between the floor and the ladder? {Hint: Use the x- and y-components of the force on the ladder by the floor.} n = normal force by the wall mg ladder Fy Fx

8. {continued} Put pivot at bottom left end to get the force n from torque: Use net force to get to Fx and Fy:

n = normal force by the wall (b) A 60.0 kg painter stands on the ladder 3.00 meters along the ladder from the bottom. Find the force exerted on the ladder by the wall and the floor. (c) If the ladder just begins to slip at its base at this point, what is the coefficient of static friction between the floor and the ladder? {Hint: Use the x- and y-components of the force on the ladder by the floor.} n = normal force by the wall Fy mg ladder mg painter Fx

8. {continued} Put pivot at bottom left end to get the force n from torque: Use net force to get to Fx and Fy:

8c. Fy is a normal force and fx is a static friction force 8c. Fy is a normal force and fx is a static friction force. The relation of the two forces is given by the definition:

9. A 5.00 m long, 20 kg beam extends out from a wall at an angle of 30.0 degrees above the horizontal. A horizontal wire reaches from the wall and attaches 1.00 m from the upper end of the beam. Find the force exerted on the beam by the wall and the tension in the wire Fy Fx

9. {continued} Put pivot at bottom left end to get the force T from torque: Use net force to get to Fx and Fy:

10. Add a 10. 0 kg mass is added to the upper end of the beam 10. Add a 10.0 kg mass is added to the upper end of the beam. Find the force on the beam by the wall and the tension in the wire. Fy Fx

10. {continued} Put pivot at bottom left end to get the force T from torque: Use net force to get to Fx and Fy:

11. 115 kg Mr. Mosig stands at the pool-end of a 25. 0 kg, 3 11. 115 kg Mr. Mosig stands at the pool-end of a 25.0 kg, 3.40 m long diving board. If the board is held to the ground by two posts, one at the end of the board and one 70.0 cm in from the end, find the forces acting on the board by each of the supports.

11. {continued} Put pivot at bottom left end to get the force T from torque: Use net force to get to F1: