Please give step-by-step solutions to the following problems.
1. A softball of mass 0.22 kg that is moving with a speed of 6.5 m/s collides head-on and elastically with another ball initially at rest. Afterward it is found that the incoming ball has bounced backward with a speed of 3.8 m/s. Calculate
a) the velocity of the target ball after the collision.
b) the mass of the target ball.
2. A wheel (radius = 0.20 m) starts from rest and rotates with a constant angular acceleration of 2.0 rad/s^2. At the instant when the angular velocity is equal to 1.2 rad/s, what is the magnitude of the total acceleration of a point on the rim of the wheel?
3. A 25-ft long crane supported at its lower end by a pin is elevated by a horizontal cable as shown in the figure. A 250-lb load is suspended from the outer end of the crane. The center of gravity of the crane is 10 ft from the pin, and the crane weighs 200 lb. What is the tension in the horizontal cable?
5. A proton traveling with speed 8.2x10^5 m/s collides elastically with a stationary proton in a hydrogen target. One of the proton is observed to be scattered at a 60 degree angle. At what angle will the second proton be observed, and what will be the velocities of the two protons after the collision?
6. The U-shaped object pictured in figure has outside dimensions of 100 mm on each side, and each of its three sides is 20 mm wide. It was cut from a uniform sheet of plastic 6.0 mm thick. Locate the center of mass of this object.
7. The angular acceleration (in rad/s^2) of a wheel, as a function of time, is alpha = 5.0 t^2 - 3.5 t . If the wheel starts from rest, determine a formula for
a) the angular velocity as a function of time.
b) the angular position as a function of time.
c) Evaluate omega and theta at t = 2.0 s.
Please refer to the attachment for mentioned figures.
Collision, angular acceleration, tension in cable, torque, and center of mass are assessed.