Physics Problem Solving: Momentum, Energy, and Forces
1. Bullet and Block Collision
a. Speed of the Bullet: The speed of the bullet when it left the barrel can be found by equating the momentum before and after the collision. The momentum of the bullet before the collision is 0.05v kg·m/s, and after the collision, it combines with the block to have a momentum of 5.05 kg·m/s. By solving the equation 0.05v = 5.05, we get the speed of the bullet.
b. Spring Period: The period of the spring can be calculated using the formula period = 2π * sqrt(mass / spring constant). Substituting the given values, we can find the period of the spring in motion.
c. Spring Position Equation: The equation for the position of the spring oscillator can be expressed as x = A * cos(2π * t / T), where x is the displacement, A is the amplitude (compression of the spring), t is the time, and T is the period of the spring.
2. Tractor Wheel Movement
a. Speed Leaving the Ramp: Utilizing the conservation of mechanical energy, we can determine the speed of the wheel when leaving the ramp by comparing initial and final mechanical energies.
b. Altitude Achieved: By setting the initial and final mechanical energies equal, we can calculate the altitude the wheel reaches during its movement.
3. Kelly and the Zombie Scenario
a. Dropping the Zombie: Kelly needs to calculate the acceleration of the platform to determine the force she exerts to drop the zombie. By applying Newton's second law of motion, she can find the distance from the right end she should be to achieve this.
b. Eyes Closed Duration: With knowledge of Kelly's mass and the force she exerts to reach a specific velocity, the time she should keep her eyes closed while running towards the zombie can be calculated.