A certain nonlinear spring has a force function given by F = −ax^2−b where x is the displacement of the spring from equilibrium, a=3.0 N/m^2 and b=4.0 N. The change in elastic potential energy of the spring as it is stretched from x= 0 m to x = 2 m is:. A. 16 J
B. 12 J
C. -8 J
D. -12 J
E. -16 J

As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. when you push the platform, you compress the springs. you do an amount of work of 79.0 j when you compress the springs a distance of 0.230 m from their uncompressed length. (a) what magnitude of force must you apply to hold the platform in this position? (b)how much additional work must you do to move the platform a distance 0.230 m farther? (c) what maximum force must you apply to move the platform a distance 0.230 m farther?

According to newton’s law of universal gravitation, which statements are true? as we move to higher altitudes, the force of gravity on us decreases. as we move to higher altitudes, the force of gravity on us increases. as we gain mass, the force of gravity on us decreases. as we gain mass, the force of gravity on us increases. as we move faster, the force of gravity on us increases.

In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5.0-m-diameter hollow steel cylinder with their backs against the wall. the cylinder begins to rotate about a vertical axis. then the floor on which the passengers are standing suddenly drops away! if all goes well, the passengers will “stick” to the wall and not slide. clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. part a what is the minimum rotational frequency, in rpm, for which the ride is safe? express your answer using two significant figures. f f = rpm