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The tray dispenser in your cafeteria has broken and is not repairable. The custodian knows that you are good at designing things and asks you to help him build a new dispenser out of spare parts he has on his workbench. The tray dispenser supports a stack of trays on a shelf that is supported by four springs, one at each corner of the shelf. Each tray is rectangular, with dimensions 45.3 cm by 35.6 cm. Each tray is 0.450 cm thick and has a mass of 580 g. The custodian asks you to design a new four-spring dispenser such that when a tray is removed, the dispenser pushes up the remaining stack so that the top tray is at the same position as the just-removed tray was. He has a wide variety of springs that he can use to build the dispenser. Which springs should he use?
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Chapter 7 Solutions
Physics for Scientists and Engineers
- The structure shown below is supported by a pin and roller on an inclined surface that is parallel to the line connecting joints A and G. Given that P = 490 lb. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 18 in.18 in.18 in.18 in.→ P| P❘ P P P E D C B 12 in. F 12 in. + H G Determine the force supported by the members CD, CI, and J. Enter forces as positive numbers if the member is in tension and as negative numbers if the member is in compression. (Round the final answers to four decimal places. Include a minus sign if necessary.) The force supported by the members CD, Cl, and IJ is as follows: FCD= FCI= lb FIJ= lb lbarrow_forwardThe drawing shows two crates that are connected by a steel wire that passes over a pulley. The unstretched length of the wire is 1.5 m, and its cross-sectional area is 1,3×10-5 m2. The pulley is frictionless and massless. When the crates are accelerating, determine the change in length of the wire. Ignore the mass of the wire.arrow_forwardA board sits in equilibrium. On the left end, there is a wire that supports the board from the ceiling, and to the right, there is a sawhorse that supports the board from the ground. The sawhorse is a distance d= 1/5l from the right edge of the board. There is a block with mass ms= 4.5kg that is a distance 3/4l from the right edge of the board. Finally the board has a mass mb= 11kg. e) What is the force of tension and normal force on the board?arrow_forward
- A board sits in equilibrium. On the left end, there is a wire that supports the board from the ceiling, and to the right, there is a sawhorse that supports the board from the ground. The sawhorse is a distance d= 1/5l from the right edge of the board. There is a block with mass ms= 4.5kg that is a distance 3/4l from the right edge of the board. Finally the board has a mass mb= 11kg. e) What is the force of tension and normal force on the board?arrow_forwardConsider the following figure. A strand has one end tied to a wall, extends across a small fixed pulley, and the other end is tied to a hanging object. M The total length of the strand is L = 9.00 m, the mass of the strand is m = 9.00 g, the mass of the hanging object is M = 7.00 kg, and the pulley is a fixed a distance d = 7.00 m from the walI. You pluck the strand between the wall and the pulley and it starts to vibrate. What is the fundamental frequency (in Hz) of its vibration? 19.40 How is the speed of the wave along the strand related to the tensions in and the linear mass density? How is the speed of the wave along the strand related to the wavelength and the frequency? See if you can combine these two relationships to determine the desired frequency. Hz Need Help? Read Itarrow_forwardA uniform 10.0 m beam of mass 300 kg extends over a ledge, as in Figure. The beam is not attached but simply rests on the surface. A 60.0 kg student intends to position the beam so that he can walk to the end of it. What is the maximum distance the beam can extend past the end of the ledge and still allow him to perform this feat?arrow_forward
- A ladder of negligible mass composed of two L-long rails that are hinged at the top, is placed on top of a frictionless floor. A metal bar, connecting both rails halfway up the ladder is placed so that the two rails make an angle of 0 = 43.0 at the apex. Lastly, a M = 4.30 [kg] block is placed 2/3 of the way up the ladder, as shown. 213 L Ө L H # A) what is the magnitude of the tension in the metal bar? B) What is the magnitude of the normal force exerted on the bottom right side of the ladder? C) What is the magnitude of the normal force exerted on the bottom left side of the ladder? D) What is the magnitude of the force the right side of the ladder exerts on its left side?arrow_forwardA frustrated farmer is trying to move a large rock from his land. The stone has a mass of 9.00×102 kg. By using a piece of board as a lever and a fulcrum the farmer will have a better chance of moving the rock. The farmer places the fulcrum 0.266 m from the rock so that the edge of the board is located directly under the center of the weight of the rock. The farmer can exert a maximum force of 632.0 N. Calculate the minimum total length of board needed to move the stone?arrow_forwardTOPIC: Applications of Integration Length of Curves Surface of Revolution Centroids of Plane Areas and Solids of Revolutions Requirements: a. Graph b. Complete Solution c. Final answer in decimal formarrow_forward
- Scissors are like a double-lever "Stem, Which of the Simple machines in Figure 9.23 and Figure 9.24 is most analogous to scissors? Figure 9.23 A nail puller is a lever with a large mechanical advantage. The external forces on the nail puller are represented by solid arrows. The force that the nail puller applies to the nail ( Fo ) is not a force on the nail puller. The reaction force the nail exerts back on the puller ( Fn ) is an external force and is equal and opposite to Fo. The perpendicular lever arms of the input and output forces are li and l0 Figure 9.24 (a) In the case of the wheelbarrow, the output force or load is between the pivot and the input force. The pivot IS the wheel's axle. Here, the output force is greater than the input force. Thus, a wheelbarrow enables you to lift much heavier loads than you could with your body alone. (b) In the case of the shovel, the input force is between the pivot and the load, but the input lever arm is shorter than the output lever arm. The pivot is at the handle held by the right hand. Here, the output force (supporting the shovel's load) is less than the input force (from the hand nearest the load), because the Input is exerted closer to the pivot than is the outputarrow_forwardConsider a rigid steel beam of length L = 13 m and mass mb = 378 kg resting on two supports, one at each end. A worker of mass mw = 61 kg sits on the beam at a distance x from support A. Refer to the figure, though note that it is not drawn to scale. Enter an expression for the force support B must exert on the beam in order for it to remain at rest, in terms of defined quantities, x, and g. FB = When the worker sits at a distance x = 8.5 m from support A, calculate the force, in newtons, that support B must exert on the beam in order for it to remain at rest. Use g with three significant figures. FB =The force exerted on the beam by support A is measured and found to be FA = 2280 N. At what distance x, in meters, from support A is the worker sitting now? x =arrow_forwardO X 1 m 25 kg 60° 6 m a uniform rod of length(1)=6m and mass(m)=66.2kg is connected by a hinge to a wall. The rod is supported in the horizontal direction by a string rope. The string rope makes an angle of 60 degrees with the ceiling. The rod holds up a 25 kg sign board with two vertical ropes which are 1 meter apart. It is known that the string rope can sustain a maximum Tension of 1200 N. Jeanluke is 75 kg . He starts at the hinge and starts walking to the end of the rod. a. Draw a force diagram of the rod. Show all the forces acting on the rod. b. Figure out the furthest position (x) from the hinge which jeanluke can stand safely c. Determine the components of the reaction force exerted by the hinge on the rod in this critical situation (when jeanluke is at position x ).arrow_forward
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