State Newton’s first law of motion in words.
A block with weight $15\,\text{N}$ is suspended by a wire from a remotely controlled aircraft, as shown in Fig. 2.1. The aircraft is used to move the block only vertically. Air resistance on the block is negligible. Fig. 2.2 shows how the block’s vertical velocity $v$ varies with time $t$. Upward motion is taken as positive.
Determine, for the block, the displacement between time $t = 0$ and $t = 3.0\,\text{s}$. State both the magnitude and the direction of the displacement.
Determine the change in gravitational potential energy between time $t = 0$ and $t = 3.0\,\text{s}$.
Calculate the magnitude of the acceleration of the block at time $t = 2.0\,\text{s}$.
Use your answer in (b)(ii) to show that the tension $T$ in the wire at time $t = 2.0\,\text{s}$ is $20\,\text{N}$.
Determine, for the block, the displacement between time $t = 0$ and $t = 3.0\,\text{s}$. Hence state both the magnitude and the direction of the displacement.
Determine the change in gravitational potential energy between time $t = 0$ and $t = 3.0\,\text{s}$.
Calculate the magnitude of the acceleration of the block at time $t = 2.0\,\text{s}$.
Use your answer in part (ii) to show that the tension $T$ in the wire at time $t = 2.0\,\text{s}$ is $20\,\text{N}$.
The wire has a cross-sectional area of $2.8 \times 10^{-5}\,\text{m}^2$ and is made from metal with Young modulus $1.7 \times 10^{11}\,\text{Pa}$. The wire obeys Hooke’s law. Calculate the strain of the wire at time $t = 2.0\,\text{s}$.
At some time after $t = 3.0\,\text{s}$ the tension in the wire has a constant value of $15\,\text{N}$. State and explain whether it is possible to deduce that the block is moving vertically after $t = 3.0\,\text{s}$.