The correct answer is B because:

The acceleration due to gravity of 9.8 m s^–2 acts downwards on Y since it is hanging freely
- Weight of Y $= m g = 5.0 \times 9.8 = 49 N$
As X is attached to Y, it will move up the slope as Y falls
So, the acceleration in the whole system is therefore not 9.8 m s^–2
We need to find the resultant acceleration which acts on the total mass in the system. The component of the weight of X will act on the system:
- $m g \sin 30 = 4.0 \times 9.8 \times \sin 30 = 19.6 N$
The weight of Y contributes a force up the slope while the component of weight of X contributes a force down the slope
Resultant force in system $= m a = 49 - 19.6 = 29.4 N$
- $(4.0 + 5.0) a = 29.4 N$
- Acceleration, $a = \frac{29.4}{9} = 3.27 m s^{- 2}$
This is the resultant acceleration on each X and Y.
Initially both X and Y are at rest. Consider the equation for uniformly accelerated motion:
- $v^{2} = u^{2} + 2 a s$ where u = 0, v = ?, s = 2.0 m and a = 3.27 m s^–2
- $v^{2} = 0 + 2 (3.27) (2)$
- $v = \sqrt{2 \times 3.27 \times 2} = 3.62 m s^{- 1}$
Kinetic energy of X $= \frac{1}{2} (4.0) {(3.62)}^{2}$
Kinetic energy of Y $= \frac{1}{2} (5.0) {(3.62)}^{2}$
Total kinetic energy of system $= \frac{1}{2} (4.0) {(3.62)}^{2} + \frac{1}{2} (5.0) {(3.62)}^{2} = 58.96 J$
- Therefore, the total kinetic energy is 59 J

Gravitational Potential Energy & Kinetic Energy (CIE A Level Physics)

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