The speed of a pitched baseball is 46.0m/s. You want to know how fast is your school's star baseball pitcher could throw. You make a pendulum with a rope and a small box lined with a thick layer of soft clay, so that the baseball would stick to the inside of the box. The rope was 0.955m long, the box with the clay had a mass of 5.64kg and the baseball had a mass of 0.350kg. The angle was recorded as 20deg. How fast did your star pitcher pitch the ball.

Question

The speed of a pitched baseball is 46.0m/s. You want to know how fast is your school's star baseball pitcher could throw. You make a pendulum with a rope and a small box lined with a thick layer of soft clay, so that the baseball would stick to the inside of the box. The rope was 0.955m long, the box with the clay had a mass of 5.64kg and the baseball had a mass of 0.350kg. The angle was recorded as 20deg. How fast did your star pitcher pitch the ball.

Ans: I am trying to use the conservation of energy and momentum separately, by first finding V' - sqrt(2gh) and substituting that into the conservation of momentum. Is that correct, I am not getting the required answer of 18.2m/s.

Answer 1

Inelastic collisions do no conserve energy, use conservation of momentum for the ball/clay impact.

m1u + m2(0) = (m1+m2)v
Solve for u when v is known (see below)

After the inelastic collision, conservation of energy would apply, once you have obtained the common velocity of the ball/clay mass, i.e. for the pendulum part of the question.

(1/2)(m1+m2)v² = (m1+m2)gR(1-cos(φ))

Solve for v.

Answer 2

Yes, you are on the right track by using the conservation of energy and momentum to find the speed of the pitcher's throw. Let's break down the steps:

1. Start by finding the gravitational potential energy of the box and clay when it reaches the highest point of its swing. Recall that the gravitational potential energy is given by U = mgh, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height.

U = (mass of box and clay) * g * (length of rope) * (1 - cos(angle))
U = 5.64 kg * 9.8 m/s² * 0.955 m * (1 - cos(20°))

2. The gravitational potential energy at the highest point is converted into kinetic energy when the box swings down and the baseball gets stuck to the clay. The kinetic energy is given by KE = 0.5mv², where m is the mass and v is the velocity.

KE = (mass of baseball) * v²

Since the baseball sticks to the clay, we can equate the kinetic energy to the gravitational potential energy:

0.5 * 0.350 kg * v² = 5.64 kg * 9.8 m/s² * 0.955 m * (1 - cos(20°))

3. Solve the equation for v. Rearrange the equation to isolate v:

v² = (5.64 kg * 9.8 m/s² * 0.955 m * (1 - cos(20°))) / (0.5 * 0.350 kg)

4. After calculating the right-hand side of the equation, take the square root to find v:

v = sqrt((5.64 kg * 9.8 m/s² * 0.955 m * (1 - cos(20°))) / (0.5 * 0.350 kg))

This should give you the speed at which your star pitcher threw the baseball. Make sure to double-check your calculations and units to ensure accuracy.