Part 1
A pitcher claims he can throw a 0.167 kg
baseball with as much momentum as a 2.43 g
bullet moving with a speed of 87735 m/s.
What must be its speed if the pitcher’s
claim is valid?
Answer in units of m/s
Part 2
What is the kinetic energy of the bullet?
Answer in units of J
Part 3
What is the kinetic energy of the ball?
Answer in units of J
Part 1:
To determine the speed of the baseball, we can use the principle of conservation of momentum. According to this principle, the momentum before the pitch must be equal to the momentum after the pitch.
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass × velocity
Let's label the mass of the baseball as m_ball and its velocity as v_ball. The mass of the bullet is given as 2.43 g, which is equal to 0.00243 kg, and its velocity is given as 87735 m/s.
Now we can set up the equation based on the conservation of momentum:
(m_ball × v_ball) = (0.00243 kg × 87735 m/s)
We want to solve for v_ball, so we divide both sides of the equation by m_ball:
v_ball = (0.00243 kg × 87735 m/s) / m_ball
Since the mass of the baseball is given as 0.167 kg, we can substitute this value into the equation:
v_ball = (0.00243 kg × 87735 m/s) / 0.167 kg
Now we can calculate the answer:
v_ball = 12.689kHz
Therefore, the speed of the baseball must be approximately 12.689 kHz (kilohertz) if the pitcher's claim is valid.
Part 2:
The kinetic energy of an object can be calculated using the formula:
Kinetic energy = (1/2) × mass × velocity^2
The mass of the bullet is given as 2.43 g, which is equal to 0.00243 kg, and its velocity is given as 87735 m/s.
Substituting these values into the formula:
Kinetic energy = (1/2) × 0.00243 kg × (87735 m/s)^2
Evaluating this expression gives:
Kinetic energy = 9235.071 J
Therefore, the kinetic energy of the bullet is approximately 9235.071 Joules.
Part 3:
To calculate the kinetic energy of the baseball, we'll use the same formula as in part 2:
Kinetic energy = (1/2) × mass × velocity^2
The mass of the baseball is given as 0.167 kg, and we found its velocity to be approximately 12.689 kHz (kilohertz) in part 1.
Substituting these values into the formula:
Kinetic energy = (1/2) × 0.167 kg × (12.689 kHz)^2
Note: It's important to convert kHz to meters per second before calculating the kinetic energy. 1 kHz is equal to 1000 Hz, and 1 Hz is equivalent to 1/s. Therefore, 1 kHz is equal to 1000/s, which is equivalent to 1000 m/s.
Converting the velocity from kilohertz to meters per second:
12.689 kHz × 1000 m/s/kHz = 12689 m/s
Now we can plug in this value and the mass of the baseball into the formula:
Kinetic energy = (1/2) × 0.167 kg × (12689 m/s)^2
Evaluating this expression gives:
Kinetic energy = 14119.237 J
Therefore, the kinetic energy of the baseball is approximately 14119.237 Joules.