1.) A tennis ball (mass = 57 grams) is held directly above a basketball (mass = 624 grams)that is held 4.7 meters off the ground. Both are dropped simultaneously. Assuming an
elastic collision, how high above the ground does the tennis ball reach after bouncing? (Note that the tennis ball bounces off the basketball which is 24 cm in diameter.)
2.)
A bullet with mass 0.050 kg is shot
through a block suspended from a cord with length 0.75 m. The block has mass
1 kg and is initially suspended
vertically a distance 1.2 meters off the floor. After the bullet goes through the block, it is observed that the block rises to an angle of 64 degrees and that the bullet lands a horizontal distance of 40.0 meters from the pendulum. What was the initial speed of the bullet?
Pi=Pf
Ki=Kf
To solve both of these problems, we can apply the principles of conservation of energy and conservation of momentum.
1.) To find out how high above the ground the tennis ball reaches after bouncing off the basketball, follow these steps:
Step 1: Calculate the initial potential energy of the system:
The potential energy of the system is given by the mass of the basketball multiplied by the acceleration due to gravity (9.8 m/s^2), multiplied by the height from which it is dropped. So, the initial potential energy of the system is:
Potential Energy = (mass of the basketball) * (acceleration due to gravity) * (height from which it is dropped)
Step 2: Calculate the initial total kinetic energy of the system:
The total kinetic energy of the system is the sum of the kinetic energies of the basketball and the tennis ball. Since both objects are initially at rest, the total kinetic energy is zero.
Step 3: Calculate the final total kinetic energy of the system:
After the tennis ball bounces off the basketball, both objects will be in motion. To find the final total kinetic energy, we need to calculate the individual kinetic energies of the basketball and the tennis ball. The kinetic energy of an object is given by 0.5 * mass * velocity^2.
Step 4: Apply conservation of energy:
According to the law of conservation of energy, the initial potential energy of the system is equal to the sum of the initial and final total kinetic energies. So, we can write the equation:
Initial Potential Energy = Initial Total Kinetic Energy + Final Total Kinetic Energy
Step 5: Calculate the final height:
By rearranging the equation from step 4, we can solve for the final height that the tennis ball reaches.
2.) To find the initial speed of the bullet, we can apply the principle of conservation of momentum and the principle of conservation of energy.
Step 1: Calculate the initial momentum of the system:
The initial momentum of the system is given by the product of the mass of the bullet and its initial velocity.
Step 2: Calculate the final momentum of the system:
After the bullet goes through the block, both the bullet and the block will be in motion. The final momentum of the system is given by the product of the final velocities of the bullet and the block.
Step 3: Apply conservation of momentum:
According to the law of conservation of momentum, the initial momentum of the system is equal to the final momentum of the system. So, we can write the equation:
Initial momentum = Final momentum
Step 4: Solve for the initial velocity of the bullet:
By rearranging the equation from step 3, we can solve for the initial velocity of the bullet.