Final answer:
The work done by air resistance on a baseball is calculated using the change in kinetic energy, which is found by subtracting the final kinetic energy from the initial kinetic energy. In the problem provided, the baseball experienced 87.5 J of work done by air resistance to slow it down from 40 m/s to 30 m/s.
Step-by-step explanation:
The subject of the question is Physics, specifically it relates to the area of mechanics involving projectile motion, energy, and work. For the given problems, students must understand and apply principles of kinematics, work-energy theorem, and conservation of energy to solve for various physical quantities such as work done by air resistance, initial velocity of a ball, average force during a collision, initial speed in a basketball shot, and trajectory equations. Let's take one example from the list of questions provided:
Work Done by Air Resistance on a Baseball
To calculate the work done on a baseball by air resistance, we use the formula W = ΔKE where W is the work done by air resistance and ΔKE is the change in kinetic energy of the object. The kinetic energy of an object is given by the formula KE = (1/2)mv2, where m is the mass and v is the velocity. In this scenario, the initial kinetic energy (KEi) when the ball is hit at 40 m/s is:
KEi = (1/2)(0.25 kg)(40 m/s)2 = 200 J
The final kinetic energy (KEf) when the ball lands at 30 m/s is:
KEf = (1/2)(0.25 kg)(30 m/s)2 = 112.5 J
Thus, the change in kinetic energy (ΔKE) is:
ΔKE = KEf - KEi = 112.5 J - 200 J = -87.5 J
The work done by air resistance is equal to the negative of the change in kinetic energy, so:
Work done by air resistance = -ΔKE = 87.5 J
This indicates that 87.5 J of work was done by air resistance to slow the ball down as it traveled from home plate to the bleachers.