Amass of 100 g stretches a spring 5 cm. if the mass is set in motion from its equilibrium position with a downward velocity of 30 cm/s, and if there is no damping, determine the position u of the mass at any time t. (use g = 9.8 m/s2 for the acceleration due to gravity. let u(t), measured positive downward, denote the displacement in meters of the mass from its equilibrium position at time t seconds.)

Find the magnetic field a distance r from the center of a long wire that has radius a and carries a uniform current per unit area j in the positive z direction.

Agroup of students were investigating the force of gravity. they began by dropping a foam ball from a height of 3 meters into a bucket of sand. the ball hit the sand in 0.306 seconds. they dropped additional balls of approximately the same diameter, but of different masses. here is the data they collected. based on this experiment and the collected data, what would their conclusion be?

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?