Physics 9702 · AS & A Level · Equilibrium of forces
Equilibrium of forces — practice question
A rigid, uniform beam of weight $W$ is joined to a fixed support by a hinge, as illustrated in Fig. 2.1. A compressed spring applies a total upward force of $8.2\,\text{N}$ to the horizontal beam. A block with weight $0.30\,\text{N}$ is resting on the beam. The beam’s right-hand end is tied to the ground by a string making an angle of $30^\circ$ to the horizontal. The tension in the string is $4.8\,\text{N}$. The distances measured along the beam are shown in Fig. 2.1. The beam is in equilibrium. Take the hinge to be frictionless.
(a(i))[1]
Show that the vertical component of the tension in the string is $2.4\,\text{N}$.
(a(ii))[3]
Determine the beam’s weight $W$ by taking moments about the hinge.
(a(iii))[1]
Calculate the horizontal component of the force exerted on the beam by the hinge.
(b)[2]
The spring follows Hooke’s law and has elastic potential energy of $0.32\,\text{J}$. Calculate the compression of the spring.
(c(i))[2]
Calculate the decrease in the gravitational potential energy of the block as it moves from A to B.
(c(ii))[3]
Use your answer in (c)(i) and conservation of energy to determine the speed of the block at point A.
(c(iii))[1]
Using the force on the block, explain why the horizontal component of the block’s velocity remains constant as it moves from A to B.
(c(iv))[1]
The block passes point A at time $t_A$ and reaches point B at time $t_B$. On Fig. 2.3, sketch a graph to show how the magnitude of the vertical velocity component $v_y$ varies with time $t$ from $t=t_A$ to $t=t_B$. Numerical values of $v_y$ are not required.
Worked solution & mark scheme
This 14-mark question has a full step-by-step worked solution and mark scheme. One marking point: “vertical component of tension $= 4.8 \sin 30^\circ = 2.4\,\mathrm{N}$” …