Bending Beams
If you bend a rod down, it compresses the lower side of the rod and stretches the top, resulting in a restoring force. Figure I.4 shows a
FIGURE 1.4
beam of length L, width w, and thickness t fixed at one end and free to move at the other. Deflecting the end of the beam causes a restoring force F at the end of the beam. The magnitude of the restoring force F depends on the dimensions of the beam, the Young’s modulus Y for the material, and the deflection d. For small values of the deflection, the restoring force is
This is similar to the formula for the restoring force of a spring, with the quantity in brackets playing the role of the spring constant k.
When a 70 kg man stands on the end of a springboard (a type of diving board), the board deflects by 4.0 cm.
If the board is replaced by one that is half the length but otherwise identical, how much will it deflect when a 70 kg man stands on the end?
A. 0.50 cm
B. 1.0 cm
C. 2.0 cm
D. 4.0 cm
Want to see the full answer?
Check out a sample textbook solutionChapter P Solutions
College Physics: A Strategic Approach (3rd Edition)
Additional Science Textbook Solutions
Life in the Universe (4th Edition)
Essential University Physics: Volume 1 (3rd Edition)
University Physics Volume 1
An Introduction to Thermal Physics
The Cosmic Perspective
College Physics: A Strategic Approach (4th Edition)
- A uniform rod of mass M and length L is attached to a pivot with negligible friction as shown. The pivot is attached to a wall and the bar starts oriented Pivot horizontally. Use the given variables and the acceleration of gravity, g, to.answer the questions symbolically. L.arrow_forwardA heavy crate needs to be moved. A crane can provide the force F at the mounting point shown. a.) Determine the moment about point A due to the force F. Enter your answer in Cartesian components with units of ft-lbs. Round to 3 significant digits. F = (100 i + 2453) lb A x α α Values for dimensions on the figure are given in the table below. R. Variable Value 39 in 35° a. MA = X F î+ k) ft-lbarrow_forwardA force of 50 N is applied at the end of a wrench handle that is 24 cm long. The force is applied in a direction perpendicular to the handle.a. What is the torque applied to the nut by the wrench?b. What would the torque be if the force were applied half way up the handle instead of at the end? Use the correct formula to get the correct answer.arrow_forward
- A uniform disk of mass 500 kg and radius 0.25 m is mounted on frictionless bearings so it can rotate freely around a vertical axis through its center (see the following figure). A cord is wrapped around the rim fo the disk and pulled with a force of 10 N. (a) How much work has the force done at the instant the disk has completed three revolutions, starting from rest? (b) Determine the torque due to the force, then calculate the work done by this torque at the instant the disk has completed three revolutions? (c) What is the angular velocity at the instant? (d) What is the power output of the force at that instant?arrow_forwardPlease write the unitsarrow_forwardForces are applied on the beam as shown on the figure at right: a. Find the torque about point P produced by each of the three forces. b. Find the net torque about point P. c. A fourth force is applied to the beam at a distance of 0.30 m to the right of point P. What must the magnitude 15 N 0.25m P 0.15m 0.2m and direction of this force be to make 20 N 5 N the beam in rotational equilibrium?arrow_forward
- A set of reducing gears is used to raise the box as shown below. Pulleys B and C are welded together. B A The diameters of Pulleys A, B and C are 58 cm, 74 cm and 18 cm, respectively. The belt connecting Pulleys A and B has a length of 535 cm. Suppose that Pulley A is rotating at 0.91 revolutions per second. Answer the following, round your answers to at least 3 significant figures and include units. a. How much time does it take the belt to make one revolution if the belt is 535 cm long? b. How much time does it take Pulley B to make one revolution? c. How fast is the box ascending, i.e. what is the vertical speed of the box?arrow_forwardTwo boys with masses of 40 kg and 60 kg stand on a horizontal frictionless surface holding the ends of a light 10-m long rod. The boys pull themselves together along the rod. When they meet the 40-kg boy will have moved what distance? O a. 5 m O b. need to know the forces they exert O d. 10 m O e. 6 marrow_forwardMyrtle pulled a lever of radius 58 cm with a force of 23.2 N.a. What is the torque if she pulled it at an angle of 90°?b. What is the torque at an angle of 30°?arrow_forward
- A tower crane (Figure 1) must always be carefully balanced so that there is no net torque tending to tip it. A particular crane at a building site is about to lift a m = 2500-kg air-conditioning unit. The crane's dimensions are shown in (Figure 2). The crane's counterweight has a mass of M = 8400 kg . Ignore the mass of the beam. Part A Where must the crane's counterweight be placed when the load is lifted from the ground? (The counterweight is usually moved automatically via sensors and motors to precisely compensate for the load.) Part B Determine the maximum load that can be lifted with this counterweight when it is placed at its full extent.arrow_forwardPhysics I Review | Constants A uniform, 255 N rod that is 1.80 m long carries a 225 N weight at its right end and an unknown weight W toward the left end (Figure 1). When W is placed 45.0 cm from the left end of the rod, the system just Part A balances horizontally when the fulcrum is located 75.0 cm from the right end. Find W. Figure 1 of 1 Express your answer with the appropriate units. W = 218 N Submit Previous Answers v Correct Correct answer is shown. Your answer 217.5 N was either rounded differently or used a different number of significant figures than required for this part. 225 N Important: If you use this answer later parts, use the full unroundedarrow_forwardPls solve this question correctly instantly in 5 min i will give u 3 like for surearrow_forward
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill