HW#27 Ch 9: Center of Mass and Linear Momentum
Instructions: Be sure to write formulas and show substitutions to earn full credit.
1. A 3.50 kg block of ice experiences a time-varying force that can be expressed as \(F(t) = 2t^2 - 4t + 4\) where force is in Newtons and time is in seconds. If the block has an initial velocity of 2 m/s in the negative direction, what is its velocity at t = 2 s? Use the impulse-momentum relationship to solve this problem.
2. A 42.7 g racquetball moving with a speed of 20.0 m/s strikes the wall at an angle of 20° with respect to the normal and then bounces off with the same speed at the same angle. It is in contact with the wall for 2 ms. What is the average force exerted by the ball on the wall?
3. Two particles of mass m1 and m2 experience a perfectly inelastic collision. If the velocity of particle 1 is v1 and the velocity of particle 2 is v2, show that the difference in total kinetic energy before and after the collision is \(\Delta K = -\dfrac{m_1m_2}{2(m_1+m_2)}(v_1 - v_2)^2\). You will need to solve for the final velocity using a momentum equation and substitute this into the final kinetic energy equation.
4. When radon decays, it produces an alpha particle (helium nucleus) with an energy of 7.69 MeV. Suppose that the alpha particle has a mass of 6.64 x 10-27 kg and an initial velocity of 1.93 x 107 m/s in the x-direction, and that it strikes a stationary gold nucleus (mass = 3.29 x 10-25 kg) head on. What are the velocities of the alpha particle and gold nucleus after the collision, if it is entirely elastic?