A pitcher claims he can throw a 0.157 kg baseball with as much momentum as a 1.5 g bullet moving with a speed of 1.50 multiplied by 103 m/s.
(a) What must the baseball's speed be if the pitcher's claim is valid?
m/s
(b) Which has greater kinetic energy, the ball or the bullet?
To determine the velocity of the baseball, we can use the principle of conservation of momentum. According to the conservation of momentum, the momentum before the pitch should 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.
Given:
Mass of the baseball (m1) = 0.157 kg
Mass of the bullet (m2) = 1.5 g = 1.5 × 10^(-3) kg
Velocity of the bullet (v2) = 1.50 × 10^3 m/s
(a) To find the velocity of the baseball (v1), we can set up the equation:
m1 * v1 = m2 * v2
Substituting the values:
0.157 kg * v1 = 1.5 × 10^(-3) kg * 1.50 × 10^3 m/s
Simplifying:
v1 = (1.5 × 10^(-3) kg * 1.50 × 10^3 m/s) / 0.157 kg
v1 ≈ 14.354 m/s
Therefore, the speed of the baseball must be approximately 14.354 m/s for the pitcher's claim to be valid.
(b) The kinetic energy of an object is given by the equation: Kinetic Energy = 0.5 * mass * velocity^2.
Comparing the kinetic energy of the ball (KE1) and the bullet (KE2):
KE1 = 0.5 * m1 * v1^2
KE2 = 0.5 * m2 * v2^2
Substituting the values:
KE1 = 0.5 * 0.157 kg * (14.354 m/s)^2
KE2 = 0.5 * 1.5 × 10^(-3) kg * (1.50 × 10^3 m/s)^2
Calculating:
KE1 ≈ 15.298 J
KE2 ≈ 1.688 J
Comparing the values, we can see that the kinetic energy of the baseball (KE1) is greater than the kinetic energy of the bullet (KE2). Therefore, the ball has greater kinetic energy than the bullet.
To find the speed of the baseball if the pitcher's claim is valid, we can start by using the formula for momentum:
Momentum = mass * velocity
Let's start by finding the momentum of the bullet. We are given the mass of the bullet (1.5 g), which we need to convert to kilograms:
1.5 g = 1.5 * 10^-3 kg
Now we can calculate the momentum of the bullet:
Momentum of the bullet = mass of the bullet * velocity of the bullet
= 1.5 * 10^-3 kg * 1.50 * 10^3 m/s
= 2.25 Ns
According to the pitcher's claim, the momentum of the baseball should be equal to the momentum of the bullet. Therefore, we can set up the equation:
Mass of the baseball * velocity of the baseball = Momentum of the bullet
0.157 kg * velocity of the baseball = 2.25 Ns
Now, solve for the velocity of the baseball:
velocity of the baseball = 2.25 Ns / 0.157 kg
= 14.33 m/s
So, the speed of the baseball has to be 14.33 m/s for the pitcher's claim to be valid.
To determine which has greater kinetic energy, we can use the equation for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Let's calculate the kinetic energy of the bullet first:
Kinetic energy of the bullet = (1/2) * 1.5 * 10^-3 kg * (1.50 * 10^3 m/s)^2
Now, calculate the kinetic energy of the baseball:
Kinetic energy of the baseball = (1/2) * 0.157 kg * (14.33 m/s)^2
Now compare the two values to determine which has greater kinetic energy.