The horizontal wire of length L = 6.00 cm hangs from two vertically-oriented springs and is immersed in a magnetic field of magnitude Bin = 0.400 T. When an object is placed on the pan of the balance, its weight is applied to a mechanical system that reduces the force by a factor of exactly 1,000. This reduced force is applied directly downward on the horizontal wire. As a result, the wire moves downward, stretching the springs. The variable power source at the upper right is controlled by software and its voltage varies until the magnetic force on the wire pulls it back upward and returns it to the original position, as measured by the springs no longer being stretched. The voltage of the power source is then used to determine the weight of the object. When there is no weight on the pan, the power source voltage is 0. The upper limit of the balance is a mass of m = 1.00 kg, for which the voltage of the power source is to be ΔV = 30.0 V. Your task is to determine the value of the resistance R (in Ω) of the circuit to assure that the power supply meets these design criteria.

Amass m = 74 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius r = 18.4 m and finally a flat straight section at the same height as the center of the loop (18.4 m off the ground). since the mass would not make it around the loop if released from the height of the top of the loop (do you know why? ) it must be released above the top of the loop-the-loop height. (assume the mass never leaves the smooth track at any point on its path.) 1. what is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? 2. what height above the ground must the mass begin to make it around the loop-the-loop? 3. if the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop? 4. if the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (18.4 m off the ground)? 5. now a spring with spring constant k = 15600 n/m is used on the final flat surface to stop the mass. how far does the spring compress?