Chapter 8: Q19PE (page 289)
Starting with the definitions of momentum and kinetic energy, derive an equation for the kinetic energy of a particle expressed as a function of its momentum.
The equation for the kinetic energy of a particle expressed as a function of its momentum is, \(K.E. = \dfrac{1}{2}pv\)
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Using mass and speed data and assuming that the football player catches the ball with his feet off the ground with both of them moving horizontally, calculate: (a) the final velocity if the ball and player are going in the same direction and (b) the loss of kinetic energy in this case. (c) Repeat parts (a) and (b) for the situation in which the ball and the player are going in opposite directions. Might the loss of kinetic energy be related to how much it hurts to catch the pass?
Two cars collide at an icy intersection and stick together afterward. The first car has a mass of\(1200 kg\)and is approaching at\(8.00\;{\rm{m/s}}\)due south. The second car has a mass of\(850 kg\)and is approaching at\(17.0\;{\rm{m/s}}\)due west. (a) Calculate the final velocity (magnitude and direction) of the cars. (b) How much kinetic energy is lost in the collision? (This energy goes into deformation of the cars.) Note that because both cars have an initial velocity, you cannot use the equations for conservation of momentum along the x-axis and y-axis; instead, you must look for other simplifying aspects.
Suppose a fireworks shell explodes, breaking into three large pieces for which air resistance is negligible. How is the motion of the center of mass affected by the explosion? How would it be affected if the pieces experienced significantly more air resistance than the intact shell?
Explain in terms of momentum and Newton’s laws how a car’s air resistance is due in part to the fact that it pushes air in its direction of motion.
During an ice show, a\(60kg\)skater leaps into the air and is caught by an initially stationary\(75kg\)skater. (a) What is their final velocityassuming negligible friction and that the\(60kg\)skater’s originalhorizontal velocity is\(4\;.00m/s\)? (b) How much kinetic energy is lost?
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