The force required to compress a non-standard spring as a function of displacement from equilibrium x is given by the equation F(x) = ax2 - bx, where a = 65 N/m2, b = 4 N/m, and the positive x direction is in the compression direction of the spring. a. Write a general equation in terms of the given variable for the work required to compress this spring from equilibrium to any point xp.

When you ride a bicycle at constant speed, nearly all the energy you expend goes into the work you do against the drag force of the air. Model a cyclist as having cross-section area 0.42 m2 and, because the human body is not aerodynamically shaped, a drag coefficient of 0.90. a.) What is the cyclist's power output while riding at a steady 7.3 m/s (16 mph)? Use 1.3 kg/m3 as a value for the density of air. P= b.) Metabolic power is the rate at which your body "burns" fuel to power your activities. For many activities, your body is roughly 25% efficient at converting the chemical energy of food into mechanical energy. What is the cyclist's metabolic power while cycling at 7.3 m/s? PM= c.) The food calorie is equivalent to 4190 J. How many calories does the cyclist burn if he rides over level ground at 7.3 m/s for 2.0 h? c=

b A marble moves along the x-axis. The potential-energy function is shown in the figure (Figure 1). d. Submit Previous Answers Correct Part C Figure 1 of 1 Which of the labeled x-coordinates is a position of unstable equilibrium? U a b d. Submit Request Answer a b c d

A 50-g mass on the end of a spring at its equilibrium position is stretched a distance of 5.00 cm and held there by a force of 10.0 N and then suddenly let go. Assume no friction.  Part A What is the speed of the mass when it returns to half of its extended position (x = 2.50 cm)?       Part B What is the speed of the mass when it returns to its equilibrium position?

A m=2.90 kg book is pushed by a completely horizontal force Fa=15.0 N a distance d=0.75m up a frictionless incline of angle theta = 25 as in Figure 1. A. Determine the work done on the book by Fa. B. Determine the work done on the book by the gravity. C. Determine the work done on the normal force. D. Determine the net work done on the book. E. If the initial velocity is vi=0 m/s, determine the final velocity of the book.

C 4. A box is being pulled across a rough floor with a force P. What can you say about the work done by pulling force, normal force, friction, and gravitational force? 0, W by normal force > 0, Wby friction 0, Why normal force 0, W by normal force= D. Wby pulling force <0, Why normal force = 0, W by friction <0, W by gravitational force = 0 0, W by friction <0. Wby gravitational force = 0

A particle of mass m moves along the x-axis. Its potential energy at any point x is, V(x) = Vox²e¬z². Vo = constant. %3D a. Find the force on the particle. b. Find all the points on the x-axis where the particle can be in equilibrium. Determine whether each equilibrium point is stable or unstable. Sketch the potential energy and label the equilibrium points.

answer D and E only

7.15 A force of 531 NN keeps a certain spring stretched a distance of 0.600 mm . 1. What is the potential energy of the spring when it is stretched 0.600 mm ? Express your answer with the appropriate units. 2. What is its potential energy when it is compressed 8.00 cmcm ? Express your answer with the appropriate units.

e A mass of 8.6 kg is lifted from the ground using a power of 72.8 W in 22.2 seconds. To what height was the mass lifted? Answer: Next page