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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
- 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_forwardEmbassy Motorcycles (EM) manufactures two lightweight motorcycles designed for easy handling and safety. The EZ-Rider model has a new engine and a low profile that make it easy to balance. The Lady-Sport model is slightly larger, uses a more traditional engine, and is specifically designed to appeal to women riders. Embassy produces the engines for both models at its Des Moines, Iowa, plant. Each EZ-Rider engine requires 6 hours of manufacturing time and each Lady-Sport engine requires 3 hours of manufacturing time. The Des Moines plant has 2100 hours of engine manufacturing time available for the next production period. Embassy’s motorcycle frame supplier can supply as many EZ-Rider frames as needed. However, the Lady-Sport frame is more complex and the supplier can only provide up to 280 Lady-Sport frames for the next production period. Final assembly and testing requires 2 hours for each EZ-Rider model and 2.5 hours for each Lady-Sport model. A maximum of 1000 hours of assembly and…arrow_forwardWhen using a ladder, it is important to place it against a wall at a safe angle. A ladder could tip over backwards if the angle is too large or the ladder could slide down the wall if the angle is too small. For a ladder to be placed at a safe angle, the ratio of the working length (how far you climb the ladder) to how far the ladder is from the wall should be 4 : 1. What angle should we place place our ladders at so that they are safe when we use them?arrow_forward
- take m and k as ; m= 0.18 kg and k = 150 n/marrow_forwardI'm not sure how to work this problem. The problem gives an answer of Itot=Icm+Md^2=18.1 kg*m^2 for part A. The problem also gives an answer of a=6.41 rad/s^2 for part B but does not show how to work the problems to get to these answers.arrow_forwardYour answer is partially correct. African elephants are the largest land animals. They consume approximately 10% of their body weight in food each day, which for an adult male, can be 1000 lb. of vegetation! Their diet consists mostly of grasses, bamboo, tree bark, and fruit. They also like to dine on tree leaves. To reach them, they often stand up on their hind legs and extend their trunks (see the figure). The elephant in the figure is in equilibrium. The location of the elephant's center of mass is shown, and the axis of rotation has been chosen to correspond to the hip joint. The forces in the elephant's free-body diagram are shown, and there is a static friction force between the elephant's back feet and the ground. Use the following information and calculate the magnitude of the tension in the elephant's trunk T (m = 4540 kg, FN = 'fs=133 cm, rcg = 76.0 cm, r = 229 cm). Number 1103.035 +x Axis of rotation Units N 165⁰ 60⁰ W =FN 30° FN 10° Michael Poliza/Caters News Agencyarrow_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_forwardEd, Edd, and Eddy love to play on a seesaw. It consists of a 1-kg board with a length of 8 meters. One day, the other end broke down. They had to cut it by a meter and maintain the pin support in its original position. Then, they tried the seesaw altogether. Ed (m = 55kg) sat on one side about 3m from the pin while Edd (m = 40kg) and Eddy (m = 40kg) on the other side. If Edd was about 3m as well from the pin, calculate the following: The manitude of the reaction force axerted by the pin support on the board. Assume Eddy is in between Ed and Edd. (mass of board = 1kg)arrow_forwardAt a construction site, there is a pile of sand in the shape of a cone. The cone has a height of 5 m and a base radius of 8 m. Suppose that the density of the sand is 1400 kg/m3. In order to assemble this pile, energy must be expended to lift each bit of sand (working against gravity) to its final height in the pile. It is known that the energy, E required to lift a mass m (in kg) to a height h (in m) is given by E = mgh (where g can be taken to be 10 m/s2). How much energy is required in total to assemble the pile?arrow_forward
- A 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_forwardYou are working with a team that is designing a new roller coaster-type amusement park ride for a major theme park. You are present for the testing of the ride, in which an empty 190 kg car is sent along the entire ride. Near the end of the ride, the car is at near rest at the top of a 102 m tall track. It then enters a final section, rolling down an undulating hill to ground level. The total length of track for this final section from the top to the ground is 250 m. For the first 230 m, a constant friction force of 400 N acts from computer-controlled brakes. For the last 20 m, which is horizontal at ground level, the computer increases the friction force to a value required for the speed to be reduced to zero just as the car arrives at the point on the track at which the passengers exit. (a) Determine the required constant friction force (in N) for the last 20 m for the empty test car. N (b) Find the highest speed (in m/s) reached by the car during the final section of track length…arrow_forwardYou are working with a team that is designing a new roller coaster-type amusement park ride for a major theme park. You are present for the testing of the ride, in which an empty 190 kg car is sent along the entire ride. Near the end of the ride, the car is at near rest at the top of a 102 m tall track. It then enters a final section, rolling down an undulating hill to ground level. The total length of track for this final section from the top to the ground is 250 m. For the first 230 m, a constant friction force of 400 N acts from computer-controlled brakes. For the last 20 m, which is horizontal at ground level, the computer increases the friction force to a value required for the speed to be reduced to zero just as the car arrives at the point on the track at which the passengers exit. (a) Determine the required constant friction force (in N) for the last 20 m for the empty test car. 4905.89 N (b) Find the highest speed (in m/s) reached by the car during the final section of track…arrow_forward
- College PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College