9.5 - explosions

why does an explosion between two objects at rest cause the objects to move away in opposite directions?

because they recoil from each other with equal and opposite amounts of momentum

what is the momentum for two objects at rest with an explosion between them?

equal and opposite to each other

what is the momentum for an object at rest?

zero

find the speeds at which these two trolleys move apart from each other

here figure 2 okay its not figure 2 but make u own question based on what it says damn bitch

here

what is the total momentum after an explosion?

• m_B v_B = - m_A v_A

• momentum of object A + momentum of object B

m_B v_B = - m_A v_A

total momentum after an explosion

derive m_B v_B = - m_A v_A

• total momentum after an explosion = m_A v_A + m_B v_B

• principle of conservation of momentum states m_A v_A + m_B v_B = 0

• rearranging gives m_B v_B = - m_A v_A

• the minus means the two masses move apart from each other in opposite directions

what does the minus sign mean in m_B v_B = - m_A v_A ?

considering this is the equation for total momentum, the minus sign signifies the two masses move apart from each other in opposite directions

what speed is an α particle emitted from an isotope?

always the same kinetic energy

why is an α particle from an isotope always emitted with the same kinetic energy?

they’re emitted with the same speed, because each α particle and the nucleus that emits it moves apart with equal and opposite amounts of momentum

what is the momentum like for an α particle emitted from an isotope?

each emitted α particle and the nucleus that emits it move apart with equal and opposite amounts of momentum

what speed is an β particle emitted from an isotope?

varied

why is the speed of a β particle emitted from an isotope varied?

• as a neutrino or antineutrino is emitted alongside the β particle, momentum is conserved in varied amounts between the products

• as mass is constant, and momentum is varied, β particle speed is varied

how can you test momentum?

using a model explosion

what’s the apparatus for testing momentum?

• two trolleys; trolley A and B

• spring loaded bolt attached to one of the trolleys

• a block behind each trolley

here

how does a test for momentum work?

1. when the spring is released from one of the trolleys, the two trolleys push each other apart

2. the blocks are positions so the trolleys hit the blocks at the same moment

how does the test for momentum prove the two trolleys carry equal amounts of momentum?

1. distance travelled = speed / time

2. time taken to hit the block is the same for both trolleys

3. therefore distance ratio = speed ratio (d_a / d_b = v_a / v_b)

4. trolleys have equal and opposite amounts of momentum

5. therefore the ratio of their speeds is the inverse of the mass ratio (v_a / v_b = m_b / m_a)

6. distance ratio = speed ratio

7. therefore distance ratio = inverse of mass ratio (d_a / d_b = m_b / m_a)

8. i.e., if A travels twice as far as B, then the mass of A must be half the mass B (so they carry away equal amounts of momentum)

for a test of momentum using trolleys, explain why (d_a / d_b = v_a / v_b)

1. distance travelled = speed / time

2. time taken to hit the block is the same for both trolleys

3. therefore distance ratio = speed ratio (d_a / d_b = v_a / v_b)

for a test of momentum using trolleys, explain why (v_a / v_b = m_b / m_a)

1. distance travelled = speed / time

2. time taken to hit the block is the same for both trolleys

3. therefore distance ratio = speed ratio (d_a / d_b = v_a / v_b)

4. trolleys have equal and opposite amounts of momentum

5. therefore the ratio of their speeds is the inverse of the mass ratio (v_a / v_b = m_b / m_a)

for a test of momentum using trolleys, explain why (d_a / d_b = m_b / m_a)

1. distance travelled = speed / time

2. time taken to hit the block is the same for both trolleys

3. therefore distance ratio = speed ratio (d_a / d_b = v_a / v_b)

4. trolleys have equal and opposite amounts of momentum

5. therefore the ratio of their speeds is the inverse of the mass ratio (v_a / v_b = m_b / m_a)

6. distance ratio = speed ratio

7. therefore distance ratio = inverse of mass ratio (d_a / d_b = m_b / m_a)

for a test of momentum using trolleys, what is the energy of the two trolleys immediately after separation?

• kinetic

• equal to the energy stores in the spring when it was originally compressed

for an explosion involving a spring, what is the energy transfer?

total kinetic energy of objects = elastic energy from spring

for a chemical explosion, what is the energy transfer?

total kinetic energy of objects immediately after explosion < total chemical energy released in the explosion

for a chemical explosion, why is total kinetic energy of objects immediately after explosion < total chemical energy released in the explosion?

because heat, light, and sound all carry away energy