Question

6. An air-track glider is connected to an ideal spring and can oscillate back and forth on the frictionless surface of the track. The potential energy function of the spring/glider system is U(x) 2.024.0 1.0 in Joules. Here represents the position of the center of the glider in meters. The graph of this function is provided. The y-axis is in Joules and the x- axis is in meters. a. What is the a-coordinate of the center of the glider when the glider is at equilibrium? b. Suppose we pull the glider to a position where it has-1.0 Joule of potential energy and release it from rest. The glider will then oscillate back and forth. What are the two coordinates of the points where the glider's center will turn around? (These coordinates are called turning points.) c. Derive the equation for the force that acts on the glider from its potential function. d. Suppose we place the glider at equilibrium and then strike it very briefly in the positive r-direction How much initial kinetic energy must we give the glider if it 's center reaches a maximum r-value of 2.5 meters just as it turns around and begins to move in the negative z-direction? For the situation described in (d), at what x-coordinate will the glider turm around and start to move in the positive a-direction? e. f. For the situation described in (d), how fast is the glider moving when it passes by z- 1.5 meter? (The mass of the glider is 200 grams.) Hint: Total energy, E, is conserved so we have E=K+ U

Answer 1

ote tivev uel posutton b)Tunning potuts au Xrom a) at a-vobu the potental Using enera ervation 1.51- KE tact to dire tion

2-5 J Tostal e a imu- 2.5T U 6.32 m