A pitcher accelerates a 150 g baseball from rest to 35 m/s. How much work does the pitcher do on the ball?

Verified step by step guidance

1. Step 1: Identify the given values in the problem. The mass of the baseball is 150 g (convert to kilograms: 0.150 kg), the initial velocity (v₀) is 0 m/s, and the final velocity (v) is 35 m/s. The goal is to calculate the work done on the ball.
2. Step 2: Recall the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy. The formula for kinetic energy is: $K_1=\frac{1}{2}m{v}^2$. The change in kinetic energy is given by: $W=K_2-K_1$.
3. Step 3: Substitute the values into the kinetic energy formula. For the initial kinetic energy, $K_1=\frac{1}{2}m{v}^2$, where $v$₀ is 0 m/s. This makes $K_1=\; 0$. For the final kinetic energy, use $K_2=\frac{1}{2}m{v}^2$, where $v$ is 35 m/s.
4. Step 4: Calculate the change in kinetic energy using the formula: $W=K_2-K_1$. Since $K_1=\; 0$, the work done is equal to $K_2$, which is $\frac{1}{2}m{v}^2$. Substitute the values for mass and velocity into this formula.
5. Step 5: Perform the calculation to find the work done. Ensure the units are consistent (mass in kilograms, velocity in meters per second), and express the result in joules (J), the standard unit of work and energy.

Key Concepts

Work-Energy Principle

The Work-Energy Principle states that the work done on an object is equal to the change in its kinetic energy. In this scenario, the pitcher does work on the baseball to accelerate it from rest to a certain speed, which results in an increase in the ball's kinetic energy.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 0.5 * m * v^2, where m is the mass and v is the velocity. For the baseball, its kinetic energy will be determined by its mass and the final speed it reaches after being pitched.

Mass and Units

Mass is a measure of the amount of matter in an object, typically measured in kilograms (kg) or grams (g). In this problem, the baseball's mass is given as 150 g, which must be converted to kilograms (0.15 kg) to use in calculations involving work and kinetic energy, as standard physics equations require SI units.