Convert units and calculate momentum and energy for each object.
a) Asteroid:
- Mass: \(m_a = 10^6 \,\mathrm{kg}\)
- Velocity: \(v_a = 500 \,\mathrm{m/s}\)
b) Train:
- Mass: \(m_b = 180,000 \,\mathrm{kg}\)
- Velocity: \(v_b = 300 \,\mathrm{km/h}\) Convert to m/s: \(v_b = \frac{300\,\mathrm{km}}{3.6\,\mathrm{h}} = 83.33\,\mathrm{m/s}\)
c) Linebacker:
- Mass: \(m_c = 120 \,\mathrm{kg}\)
- Velocity: \(v_c = 10\,\mathrm{m/s}\)
d) Cannonball:
- Mass: \(m_d = 10 \,\mathrm{kg}\)
- Velocity: \(v_d = 120 \,\mathrm{m/s}\)
e) Proton:
- Mass: \(m_e = 6 \cdot 10^{-27} \,\mathrm{kg}\)
- Velocity: \(v_e = 2 \cdot 10^8 \,\mathrm{m/s}\)
Now, calculate the momentum and energy for each object:
Object a:
\(p_a = m_a \cdot v_a = 10^6 \,\mathrm{kg} \cdot 500 \,\mathrm{m/s} = 5 \cdot 10^8\,\mathrm{kg\cdot m/s}\)
\(E_a = \frac{1}{2} \cdot m_a \cdot v_a^2 = \frac{1}{2} \cdot 10^6 \,\mathrm{kg} \cdot (500 \,\mathrm{m/s})^2 = 1.25 \cdot 10^{11}\,\mathrm{J}\)
Object b:
\(p_b = m_b \cdot v_b = 180,000 \,\mathrm{kg} \cdot 83.33 \,\mathrm{m/s} = 1.5 \cdot 10^7\,\mathrm{kg\cdot m/s}\)
\(E_b = \frac{1}{2} \cdot m_b \cdot v_b^2 = \frac{1}{2} \cdot 180,000 \,\mathrm{kg} \cdot (83.33 \,\mathrm{m/s})^2 = 6.25 \cdot 10^8\,\mathrm{J}\)
Object c:
\(p_c = m_c \cdot v_c = 120 \,\mathrm{kg} \cdot 10 \,\mathrm{m/s} = 1200\,\mathrm{kg\cdot m/s}\)
\(E_c = \frac{1}{2} \cdot m_c \cdot v_c^2 = \frac{1}{2} \cdot 120 \,\mathrm{kg} \cdot (10 \,\mathrm{m/s})^2 = 6,000\,\mathrm{J}\)
Object d:
\(p_d = m_d \cdot v_d = 10 \,\mathrm{kg} \cdot 120 \,\mathrm{m/s} = 1200\,\mathrm{kg\cdot m/s}\)
\(E_d = \frac{1}{2} \cdot m_d \cdot v_d^2 = \frac{1}{2} \cdot 10 \,\mathrm{kg} \cdot (120 \,\mathrm{m/s})^2 = 72,000\,\mathrm{J}\)
Object e:
\(p_e = m_e \cdot v_e = 6 \cdot 10^{-27} \,\mathrm{kg} \cdot 2 \cdot 10^8 \,\mathrm{m/s} = 1.2 \cdot 10^{-18}\,\mathrm{kg\cdot m/s}\)
\(E_e = \frac{1}{2} \cdot m_e \cdot v_e^2 = \frac{1}{2} \cdot 6 \cdot 10^{-27} \,\mathrm{kg} \cdot (2 \cdot 10^8 \,\mathrm{m/s})^2 = 1.2 \cdot 10^{-10}\,\mathrm{J}\)
