PH 121 Practice Final - Refined Format PDF

PH 121 Practice Final - Refined Format Practice Final Questions 1. **Position and Velocity Calculation** A particle starts from rest at position \( \vec{r}_0 = (0, 0, 0) \) m and accelerates uniformly with \( \vec{a} = (2, -1, 0) \) m/s². Find: - The po...

PH 121 Practice Final - Refined Format Practice Final Questions 1. **Position and Velocity Calculation** A particle starts from rest at position \( \vec{r}_0 = (0, 0, 0) \) m and accelerates uniformly with \( \vec{a} = (2, -1, 0) \) m/s². Find: - The position \( \vec{r}(t) \) at \( t = 5 \) seconds. - The velocity \( \vec{v}(t) \) at \( t = 5 \) seconds. 2. **Projectile Motion** A ball is thrown upward with an initial velocity of 20 m/s. Assume \( g = 9.8 \) m/s². Calculate: - The maximum height. - The total time the ball spends in the air. 3. **Kinetic Energy and Momentum** A 0.5 kg object moves with a velocity of 10 m/s. Using the formulas: - \( KE = \frac{1}{2}mv^2 \) (Kinetic Energy) - \( p = mv \) (Momentum), Calculate both the kinetic energy and momentum. 4. **Circular Motion** An object moves in a circle with radius 3 m at a constant speed of 4 m/s. Find its centripetal acceleration using: \[ a_c = \frac{v^2}{r} \] 5. **Work-Energy Theorem** A 10 kg mass is pushed by a force of 50 N over a distance of 3 m. Calculate the work done using: \[ W = F \cdot d \] Page 1  PH 121 Practice Final - Refined Format 6. **Elastic Collision** Two carts collide elastically. Cart 1 has a mass of 2 kg and moves at 3 m/s, while cart 2 has a mass of 1 kg and is stationary. Using: \[ m_1v_1 + m_2v_2 = m_1v_1' + m_2v_2' \] Determine the velocities of both carts after the collision. 7. **Spring Potential Energy** A spring with a spring constant \( k = 200 \) N/m is compressed by 0.1 m. Find the potential energy stored using: \[ PE_{spring} = \frac{1}{2}kx^2 \] 8. **Rotational Dynamics** A 1 kg disk rotates with angular acceleration \( \alpha = 2 \) rad/s² under a torque of \( \tau = 4 \) Nm. Verify: \[ \tau = I \alpha \] Assume \( I = \frac{1}{2}mR^2 \) with \( R = 0.5 \) m. 9. **Heat Calculation** A 2 kg block of aluminum (specific heat \( c = 900 \) J/kg·°C) is heated from 20°C to 80°C. Find the heat required using: \[ Q = mc\Delta T \] 10. **Pendulum Period** A pendulum with length 2 m swings with small amplitude. Find its period using: \[ T = 2\pi\sqrt{\frac{L}{g}} \] Assume \( g = 9.8 \) m/s². Page 2