Problem structure
(a) 3 marks, Numerical, Kinematics (3.1.1a).
(b) 5 marks, Numerical, Conservation of Energy and Hooke's Law (3.3.1c, 3.4.1b/c).
(c) 2 marks, Numerical/Qualitative, Work Done (3.3.1a/b).
Plan your route before writing. Use equations, diagrams, units, and a clear final justification where needed.
A testing rig uses a heavy block of mass $M = 12.0\text{ kg}$ to calibrate a vertical safety spring. The block is initially held at rest against the top of the spring. When released, the block compresses the spring.
(a)
3 marks
The block is released from rest and undergoes a constant acceleration of $a = 8.20\text{ m s}^{-2}$ downwards for the first $0.150\text{ s}$ before it makes full contact with the spring's main resistance. Calculate the displacement of the block during this initial time interval and its instantaneous velocity at $t = 0.150\text{ s}$.
(b)
5 marks
After the initial $0.150\text{ s}$, the block begins to compress the spring. The spring obeys Hooke’s Law and has a force constant $k = 4500\text{ N m}^{-1}$. The block comes to a momentary rest when the spring has been compressed by a distance $x$. By considering the principle of conservation of energy from the moment the block was first released, calculate the maximum compression $x$ of the spring. Assume air resistance is negligible and the gravitational potential energy is lost over the total vertical distance moved.
(c)
2 marks
A sensor records the force $F$ exerted by the spring on the block. Calculate the work done by the spring on the block during the compression $x$ found in part (b). State the direction of this work relative to the displacement of the block.
