State what the centre of gravity of an object means.
Two blocks rest on a horizontal beam pivoted at its centre of gravity, as shown in Fig. 2.1. A large block weighing $54\ \text{N}$ is $0.45\ \text{m}$ from the pivot. A small block weighing $2.4\ \text{N}$ is $0.95\ \text{m}$ from the pivot and $0.35\ \text{m}$ from the beam's right-hand end. The beam's right-hand end is tied to the ground by a string inclined at $30^{\circ}$ to the horizontal. The beam is in equilibrium.\n\n(i) Taking moments about the pivot, calculate the tension $T$ in the string.\n\n(ii) The string is cut, so the beam is no longer in equilibrium. Calculate the size of the resultant moment about the pivot acting on the beam immediately after the cut.
Taking moments about the pivot, calculate the tension $T$ in the string.
The string is cut, so the beam is no longer in equilibrium. Calculate the size of the resultant moment about the pivot acting on the beam immediately after the cut.
In (b) the beam turns as the string is cut, and the small block of weight $2.4\,\text{N}$ is launched through the air. Fig. 2.2 shows the final part of the block's path before it lands at point $Y$. At point $X$ on the path, the block has speed $3.4\,\text{m s}^{-1}$ and is $1.8\,\text{m}$ above the horizontal ground. Air resistance can be ignored.
Calculate the decrease in the gravitational potential energy of the block as it moves from $X$ to $Y$.
Use your answer to (c)(i) together with conservation of energy to find the kinetic energy of the block at $Y$.
State the change, if any, in the direction of the block's acceleration as it moves from $X$ to $Y$.
The block passes point $X$ at time $t_X$ and reaches point $Y$ at time $t_Y$. On Fig. 2.3, sketch a graph to show how the magnitude of the horizontal component of the block's velocity varies with time from $t_X$ to $t_Y$. Numerical values are not required.