Chapter 7: Problem 112
A Super Ball is dropped from a height of \(3.935 \mathrm{~m}\). Its maximum height on its third bounce is \(2.621 \mathrm{~m}\). What is the coefficient of restitution of the ball?
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A method for determining the chemical composition of a material is Rutherford backscattering (RBS), named for the scientist who first discovered that an atom contains a high-density positively charged nucleus, rather than having positive charge distributed uniformly throughout (see Chapter 39 ). In \(\mathrm{RBS}\), alpha particles are shot straight at a target material, and the energy of the alpha particles that bounce directly back is measured. An alpha particle has a mass of \(6.65 \cdot 10^{-27} \mathrm{~kg}\). An alpha particle having an initial kinetic energy of \(2.00 \mathrm{MeV}\) collides elastically with atom \(\mathrm{X}\). If the backscattered alpha particle's kinetic energy is \(1.59 \mathrm{MeV}\), what is the mass of atom X? Assume that atom X is initially at rest. You will need to find the square root of an expression, which will result in two possible answers (if \(a=b^{2},\) then \(b=\pm \sqrt{a}\) ). Since you know that atom \(X\) is more massive than the alpha particle, you can choose the correct root accordingly. What element is atom \(\mathrm{X} ?\) (Check a periodic table of elements, where atomic mass is listed as the mass in grams of 1 mol of atoms, which is \(6.02 \cdot 10^{23}\) atoms.
A hockey puck \(\left(m=170 . g\right.\) and \(v_{0}=2.00 \mathrm{~m} / \mathrm{s}\) ) slides without friction on the ice and hits the rink board at \(30.0^{\circ}\) with respect to the normal. The puck bounces off the board at a \(40.0^{\circ}\) angle with respect to the normal. What is the coefficient of restitution for the puck? What is the ratio of the puck's final kinetic energy to its initial kinetic energy?
A particle \(\left(M_{1}=1.00 \mathrm{~kg}\right)\) moving at \(30.0^{\circ}\) downward from the horizontal with \(v_{1}=2.50 \mathrm{~m} / \mathrm{s}\) hits a second particle \(\left(M_{2}=2.00 \mathrm{~kg}\right)\) which is at rest. After the collision, the speed of \(M_{1}\) is reduced to \(0.500 \mathrm{~m} / \mathrm{s},\) and it is moving to the left and at an angle of \(32.0^{\circ}\) downward withrespect to the horizontal. You cannot assume that the collision is elastic. What is the speed of \(M_{2}\) after the collision?
For a totally elastic collision between two objects, which of the following statements is (are) true? a) The total mechanical energy is conserved. b) The total kinetic energy is conserved. c) The total momentum is conserved. d) The momentum of each object is conserved. e) The kinetic energy of each object is conserved.
Astronauts are playing catch on the International Space Station. One \(55.0-\mathrm{kg}\) astronaut, initially at rest, throws a baseball of mass \(0.145 \mathrm{~kg}\) at a speed of \(31.3 \mathrm{~m} / \mathrm{s}\). At what speed does the astronaut recoil?
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