Mechanics Paper 4 November 2009

A block of mass 3.5 kg is released from rest at point A on a plane inclined at angle $\alpha$ to the horizontal, where $\tan\alpha = \dfrac{3}{4}$. It slides down to point B at the base of the plane. The coefficient of friction between the block and the plane is $\dfrac{1}{4}$. Take $g = 9.81$ ms$^{-2}$.

Calculate the acceleration of the block down the plane, in ms$^{-2}$.

A block of mass 3.5 kg is released from rest at point A on a plane inclined at angle $\alpha$ to the horizontal, where $\tan\alpha = \dfrac{3}{4}$. It slides down to point B at the base of the plane. The coefficient of friction between the block and the plane is $\dfrac{1}{4}$. Take $g = 9.81$ ms$^{-2}$.

The block slides 5 m down the plane from A to B. Calculate the velocity of the block at B, in ms$^{-1}$.

A block of mass 3.5 kg is released from rest at point A on a plane inclined at angle $\alpha$ to the horizontal, where $\tan\alpha = \dfrac{3}{4}$. It slides down to point B at the base of the plane. The coefficient of friction between the block and the plane is $\dfrac{1}{4}$. Take $g = 9.81$ ms$^{-2}$.

The block slides 5 m down the plane from A to B, reaching B at 6.264 ms$^{-1}$. Calculate the time it takes to slide from A to B, in seconds.

A ring of mass m kg accelerates at 1 ms$^{-2}$ along a rough horizontal wire. The accelerating force of 6 N acts at 60$^{\circ}$ above the wire, in the same vertical plane as the wire. The coefficient of friction between the ring and the wire is $\dfrac{1}{4}$.

Which expression gives the normal reaction R between the ring and the wire?

A ring of mass m kg accelerates along a rough horizontal wire. The normal reaction between the ring and the wire is $R = mg - 3\sqrt{3}$ newtons and the coefficient of friction between the ring and the wire is $\dfrac{1}{4}$.

Which expression gives the frictional force acting on the ring?

A ring of mass m kg accelerates at 1 ms$^{-2}$ along a rough horizontal wire. The accelerating force of 6 N acts at 60$^{\circ}$ above the wire, in the same vertical plane as the wire. The coefficient of friction between the ring and the wire is $\dfrac{1}{4}$.

Find the value of m, giving your answer to 3 decimal places.

A particle is projected from a point O on the ground with speed V ms$^{-1}$ at 60$^{\circ}$ to the horizontal. It passes through the point $A(\sqrt{3};\ 2)$ on its way up, and reaches its maximum height above O at the point B.

Express $V^{2}$ in terms of g.

A particle is projected from a point O on the ground at 60$^{\circ}$ to the horizontal with speed V ms$^{-1}$, and its speed satisfies $V^{2} = 6g$. Take $g = 9.81$ ms$^{-2}$.

Find the speed of projection V, in ms$^{-1}$.

A particle is projected from a point O on the ground at 60$^{\circ}$ to the horizontal with speed V ms$^{-1}$, where $V^{2} = 6g$. B is the point at which the particle reaches its maximum height above O.

Find the maximum height reached, that is the y coordinate of B, in metres.

A particle is projected from O at 60$^{\circ}$ to the horizontal with $V^{2} = 6g$. It passes through $A(\sqrt{3};\ 2)$ and reaches its maximum height at $B\left(\dfrac{3\sqrt{3}}{2};\ 2.25\right)$.

Find the angle, to the nearest degree, that the straight line AB makes with the horizontal.