If we assume that M87* is not rotating (although it definitely IS rotating but this assumption gives us a much easier calculation that can be done quickly), what is the size of its event horizon (i. e., its Schwarzschild radius)? The Schwarzschild radius of a black hole is given by LaTeX: r_{s\:}=\frac{\:2GM}{c^2}r s = 2 G M c 2 The mass of the black hole is LaTeX: 6.5\:\times10^{9\:}\:\mathrm{M_{\od ot}}6.5 × 10 9 M ⊙, where the solar mass is LaTeX: M_{\odot}\:=\:2\:\times10^{30}\:kgM ⊙ = 2 × 10 30 k g Give your answer in AU. For reference, LaTeX: 1\:AU\:=\:1.5\:\times10^{11}\:m1 A U = 1.5 × 10 11 m and the gravitational constant is LaTeX: G\:=\:6.67\:\times10^{-11}\:\:m^{3\ :}kg^{-1}s^{-2}G = 6.67 × 10 − 11 m 3 k g − 1 s − 2 You should also read over section 2.1 in the lab script. Be careful with your units! Do not use equation 1 in the lab script; that equation uses an older estimate of the black hole's mass.

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?