Please use 3 SF only (:
OT d A ladder of length L is mounted onto a wall at its lower end, while its upper end is held in place by a cable anchored to cable the same wall. The ladder makes an angle OL with the horizontal, and the cable makes an angle 01 (T for tension; see below) with the ladder. Someone is standing on the ladder, a distance d from its lower end. Everything is at rest. wall ladder 1. Choose a length L for the ladder, from 3-7 m, and the distance d, which should be 20-40% of L (if your age in years is even) or 60-80% of L (odd age). Choose a mass ML BL for the ladder (20-60 kg) and a reasonable mass Mp for the person. Finally choose the angles . (15-35) and 01 (40- 60). Round all of your choices to 3 SF and list them here. 2. Draw a large FBD for the ladder, making it as long and narrow as you can; tilted, not horizontal. The FBD should not show the person, the wall , or the cable, just the forces acting on the ladder due to these objects, and a torque axis (dot) located at the lower end of the ladder . For now, don't put in x or y axes, or the components of any force - just draw the "whole" forces and leave it at that. Required force symbols: Fw (force from the wall; it's NOT parallel to the ladder, and it's not horizontal), F, (cable tension), Fo (gravitational force acting on the ladder), and Fp (force the person exerts on the ladder, equal in magnitude to the gravitational force acting on him or her). 3. FG and Fp can be directly calculated without need for N2L, leaving just Fw and Fy unknown. I'm going to ask you to calculate the unknown cable tension force F, first, using N2L for torques, and that's why I asked you to place the torque axis at the lower end of the ladder. Explain why it would be impossible to find F, first if I'd asked you to place the torque axis at the center of the ladder, instead. 4. Calculate the angles between the ladder and FG, Fp. Add both to the FBD. Hint: look for right triangles. 5. Use your FBD and N2L for torques to calculate the tension force Ft in the cable holding the ladder, using the torque axis at the lower end of the ladder. You won't be able to solve this using N2L for forces; going with torques is the only way. Since the definition of torque involves sine, not cosine, no cosines should appear in your work. 6. Now add standard x/y axes (horizontal/vertical) to the FBD, and draw the x/y components of Fw and Ft. Then use N2L for forces to calculate the magnitude of Fw from its x and y components. Caution: 0 isn't the angle between Fr and the horizontal! If you're skeptical about my claim that Fw isn't parallel to the ladder, good! You can check it out by calculating the direction of Fw from its components, as an angle from the horizontal, and compare to 0. This is not at all required for the assignment. OT d A ladder of length L is mounted onto a wall at its lower end, while its upper end is held in place by a cable anchored to cable the same wall. The ladder makes an angle OL with the horizontal, and the cable makes an angle 01 (T for tension; see below) with the ladder. Someone is standing on the ladder, a distance d from its lower end. Everything is at rest. wall ladder 1. Choose a length L for the ladder, from 3-7 m, and the distance d, which should be 20-40% of L (if your age in years is even) or 60-80% of L (odd age). Choose a mass ML BL for the ladder (20-60 kg) and a reasonable mass Mp for the person. Finally choose the angles . (15-35) and 01 (40- 60). Round all of your choices to 3 SF and list them here. 2. Draw a large FBD for the ladder, making it as long and narrow as you can; tilted, not horizontal. The FBD should not show the person, the wall , or the cable, just the forces acting on the ladder due to these objects, and a torque axis (dot) located at the lower end of the ladder . For now, don't put in x or y axes, or the components of any force - just draw the "whole" forces and leave it at that. Required force symbols: Fw (force from the wall; it's NOT parallel to the ladder, and it's not horizontal), F, (cable tension), Fo (gravitational force acting on the ladder), and Fp (force the person exerts on the ladder, equal in magnitude to the gravitational force acting on him or her). 3. FG and Fp can be directly calculated without need for N2L, leaving just Fw and Fy unknown. I'm going to ask you to calculate the unknown cable tension force F, first, using N2L for torques, and that's why I asked you to place the torque axis at the lower end of the ladder. Explain why it would be impossible to find F, first if I'd asked you to place the torque axis at the center of the ladder, instead. 4. Calculate the angles between the ladder and FG, Fp. Add both to the FBD. Hint: look for right triangles. 5. Use your FBD and N2L for torques to calculate the tension force Ft in the cable holding the ladder, using the torque axis at the lower end of the ladder. You won't be able to solve this using N2L for forces; going with torques is the only way. Since the definition of torque involves sine, not cosine, no cosines should appear in your work. 6. Now add standard x/y axes (horizontal/vertical) to the FBD, and draw the x/y components of Fw and Ft. Then use N2L for forces to calculate the magnitude of Fw from its x and y components. Caution: 0 isn't the angle between Fr and the horizontal! If you're skeptical about my claim that Fw isn't parallel to the ladder, good! You can check it out by calculating the direction of Fw from its components, as an angle from the horizontal, and compare to 0. This is not at all required for the assignment
