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A block of mass m is placed on a smooth inclined plane, which is at an angle, with respect to the horizontal, as shown in Figure 2. A spring with force constant k is attached to the bottom of the incline. spring. block Hellll Ꮎ Figure 2 Sketch of the block, inclined plane and spring, for use in Question 9. When the block makes contact with the spring, it has a speed of v. In this part of the question, you may find it helpful to take the lowest position of the block (i.e. the height of the block at the point of maximum compression) as the reference point for zero gravitational potential energy. (i) Write an expression for the total energy of the block and spring system at the moment the block makes contact with the spring. (ii) Write an expression for the total energy of the block and spring system at the moment the spring reaches its maximum compression. (iii) Starting from conservation of energy and equating the expressions you gave in (i) and (ii), show that the maximum spring compression, D, satisfies the following quadratic equation. 1 1½ kD² - gm sin (0)D — — — — mv² = 0 - 2 2

A block of mass m is placed on a smooth inclined plane, which is at an angle, with respect to the horizontal, as shown in Figure 2. A spring with force constant k is attached to the bottom of the incline. spring. block Hellll Ꮎ Figure 2 Sketch of the block, inclined plane and spring, for use in Question 9. When the block makes contact with the spring, it has a speed of v. In this part of the question, you may find it helpful to take the lowest position of the block (i.e. the height of the block at the point of maximum compression) as the reference point for zero gravitational potential energy. (i) Write an expression for the total energy of the block and spring system at the moment the block makes contact with the spring. (ii) Write an expression for the total energy of the block and spring system at the moment the spring reaches its maximum compression. (iii) Starting from conservation of energy and equating the expressions you gave in (i) and (ii), show that the maximum spring compression, D, satisfies the following quadratic equation. 1 1½ kD² - gm sin (0)D — — — — mv² = 0 - 2 2

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A block of mass m is placed on a smooth inclined plane, which is at an angle, with respect to the horizontal, as shown in Figure 2. A spring with force constant k is attached to the bottom of the incline. spring. block Hellll Ꮎ Figure 2 Sketch of the block, inclined plane and spring, for use in Question 9.
Transcribed Image Text:A block of mass m is placed on a smooth inclined plane, which is at an angle, with respect to the horizontal, as shown in Figure 2. A spring with force constant k is attached to the bottom of the incline. spring. block Hellll Ꮎ Figure 2 Sketch of the block, inclined plane and spring, for use in Question 9.
When the block makes contact with the spring, it has a speed of v. In this part of the question, you may find it helpful to take the lowest position of the block (i.e. the height of the block at the point of maximum compression) as the reference point for zero gravitational potential energy. (i) Write an expression for the total energy of the block and spring system at the moment the block makes contact with the spring. (ii) Write an expression for the total energy of the block and spring system at the moment the spring reaches its maximum compression. (iii) Starting from conservation of energy and equating the expressions you gave in (i) and (ii), show that the maximum spring compression, D, satisfies the following quadratic equation. 1 1½ kD² - gm sin (0)D — — — — mv² = 0 - 2 2
Transcribed Image Text:When the block makes contact with the spring, it has a speed of v. In this part of the question, you may find it helpful to take the lowest position of the block (i.e. the height of the block at the point of maximum compression) as the reference point for zero gravitational potential energy. (i) Write an expression for the total energy of the block and spring system at the moment the block makes contact with the spring. (ii) Write an expression for the total energy of the block and spring system at the moment the spring reaches its maximum compression. (iii) Starting from conservation of energy and equating the expressions you gave in (i) and (ii), show that the maximum spring compression, D, satisfies the following quadratic equation. 1 1½ kD² - gm sin (0)D — — — — mv² = 0 - 2 2
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