what minimum work is required to get the cylinder rolling without slipping at a rotational speed of 20 s−1 ?

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?

Would it be correct to say the doppler effect is the apparent change in the speed of a wave due to the motion of the source? be sure to fully explain your position using at least 3 complete content related sentences.

Ultraviolet radiation is dangerous because it has a high enough energy to damage skin cells. what is the best explanation of the relationship between wavelength and wave energy? a) wave energy is related only to frequency, not wavelength. b) longer wavelengths have lower frequencies but higher energy. c) the shorter the wavelength, the lower the frequency and the higher the energy. d) the shorter the wavelength, the higher the frequency and the higher the energy.