A pitcher claims he can throw a 0.146 kg
baseball with as much momentum as a 3.37 g
bullet moving with a speed of 15238 m/s.
What must be its speed if the pitcher’s
claim is valid?
Answer in units of m/s
What is the kinetic energy of the bullet?
Answer in units of J
What is the kinetic energy of the ball?
Answer in units of J
a. m1*V1 = m2*V2,
0.146*V1 = 0.00337*15238 = 51.35,
V1 = 351.7 m/s.
b. KE = 0.5m*V^2
KE = 0.5*0.00337*(15238)^2 = 391,251 J.
c. KE = 0.5*0.146*(351.7)^2 = 9.030 J.
To determine the speed of the baseball that would give it the same momentum as a 3.37 g bullet moving at 15238 m/s, we can use the concept of momentum. The momentum (p) of an object is given by the mass (m) multiplied by the velocity (v).
For the baseball, we know the mass (m) is 0.146 kg. Let's denote the velocity of the baseball as v1. The momentum (p1) of the baseball can then be calculated as:
p1 = m * v1
For the bullet, we know the mass (m) is 3.37 g, which is equivalent to 0.00337 kg. The velocity (v) is given as 15238 m/s. Let's denote the momentum of the bullet as p2. The momentum (p2) of the bullet is then:
p2 = m * v
Since the pitcher's claim states that the momentum of the baseball is the same as the bullet's momentum, we can equate p1 and p2:
p1 = p2
m * v1 = m * v
Simplifying the equation, we can divide both sides of the equation by m:
v1 = v
Therefore, in order for the pitcher's claim to be valid, the speed of the baseball (v1) must be the same as the speed of the bullet (v), which is 15238 m/s.
To calculate the kinetic energy of the bullet, we can use the formula:
Kinetic Energy = (1/2) * m * v^2
Given that the mass (m) is 3.37 g (0.00337 kg) and the velocity (v) is 15238 m/s, we can substitute these values into the formula:
Kinetic Energy = (1/2) * (0.00337 kg) * (15238 m/s)^2
Calculating the result, we find the kinetic energy of the bullet to be approximately 77.2 J (Joules).
To calculate the kinetic energy of the baseball, we can use the same formula:
Kinetic Energy = (1/2) * m * v^2
Given that the mass (m) of the baseball is 0.146 kg and we need to find the velocity (v1), using the previous conclusion that v1 = v (15238 m/s), we can substitute these values into the formula:
Kinetic Energy = (1/2) * (0.146 kg) * (15238 m/s)^2
Calculating the result, we find the kinetic energy of the baseball to be approximately 15822 J (Joules).