In an explosion
Newton's Laws & Momentum - OCR A-Level Physics
- In an explosion, the total momentum before is zero (objects are initially at rest)
- By conservation of momentumIn a closed system (no external forces), the total momentum before an event equals the total momentum after., the total momentum after must also be zero
- The objects move in opposite directions with momenta of equal magnitude: m_1 $v_{1} = -m_{2} v_{2}$
- The lighter object always moves faster than the heavier object
- KE is NOT conserved in explosions: KE increases (energyThe capacity to do work. Measured in joules (J). comes from chemical, nuclear or elastic PE stored in the system)
$$0 = m_1 v_1 + m_2 v_2$$
Worked Example [3 marks]
A 4.0 kg cannon fires a 0.020 kg ball at 200 $m s^{-1}$. Calculate the recoil velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. of the cannon.
Show Solution
1
$Total momentum before = 0 (both at rest). By conservation: 0 = m_{cannon}v_{cannon} + m_{ball}v_{ball}$
[1]2
$0 = (4.0)(v_{cannon}) + (0.020)(200) = 4.0 v_{cannon} + 4.0$
[1]3
$v_{cannon} = \frac{-4.0}{4.0} = -1.0 \text{ m s}^{-1}. The negative sign shows the cannon recoils in the opposite direction to the ball$
[1]Answer
1.0 $m s^{-1}$ in the opposite direction to the ball
Examiner Tips and Tricks
- In explosion questions, remember that kinetic energyThe capacity to do work. Measured in joules (J).The energyThe capacity to do work. Measured in joules (J). an object possesses due to its motion. INCREASES (it was zero before).
- Energy is released from internal stores.
- Never write 'KE is conserved' in an explosion.