7. (i) State Newton's second law of motion - Leaving Cert Physics - Question 7 - 2021

The principle of conservation of momentum states that within an isolated system, the total momentum before any interaction is equal to the total momentum after that interaction. This can be expressed as:

$ext{momentum before interaction} = ext{momentum after interaction}$

The principle of conservation of energy states that energy cannot be created or destroyed; it can only be converted from one form to another. In a closed system, the total energy remains constant, meaning that the total energy before an event is equal to the total energy after the event.

Using the formula for force, we calculate the force exerted by B on A during the collision as follows:

$F = m(v_f - v_i) / t$

Where:

• $m = 0.045$ kg (mass of A),
• $v_f = 1.1$ m/s (final velocity of A),
• $v_i = 0.6$ m/s (initial velocity of A),
• $t = 0.025$ s (time of contact).

Substituting the values: $F = 0.045 imes (1.1 - 0.642) / 0.025 = 13.14 ext{ N}$

The maximum velocity of B can be calculated using the principle of conservation of momentum. Therefore:

$m_A v_A + m_B v_B = m_A v_A' + m_B v_B'$

Substituting the known values:

The maximum centripetal force is given by the formula:

F_c = rac{mv^2}{r}

where:

• $m = 0.08$ kg (mass of B),
• $v = 4.11 ext{ m/s}$ (velocity of B),
• $r = 1.2 / 1.2 ext{ m}$.

Substituting the values:

$F_c = 0.08 imes (4.11)^2 / 1.2 = 0.08/1.2 = 0.67 N$

To find the maximum height gained by B, we can use energy conservation:

$E_p = E_k$

Thus,

The angular displacement can be calculated using the cosine rule:

The diagram should show the force of gravity acting downward (labelled as weight) and the tension from the string acting vertically upwards when B is at its maximum height.

After the string is cut, the only force acting on B is gravity. Therefore, the magnitude of the acceleration is equal to the acceleration due to gravity:

$a = 9.8 ext{ m/s}^2$

The direction of the acceleration is downwards.