Mechanics | Relativity Answers

A wheel 2.0 m in diameter lies in the vertical plane and rotates about its central axis
with a constant angular acceleration of 4.0rads .
2
The wheel starts from rest at
t  0 and the radius vector of a point A on the wheel makes an angle of 60º with the
horizontal at this instant. Calculate the angular speed of the wheel, the angular
position of the point A and the total acceleration at t  2.0s.

The bulk modulus of a block of copper is 1.3 GPa. When a pressure of 1.8 MPa is applied to the 1.0 m^3 block, its volume decreases by how much?

Calculate the depth in the ocean at which the pressure is three times atmospheric pressure. Atmospheric pressure is 1.013 × 105 Pa. The acceleration of gravity is 9.81 m/s2 and the density of sea water is 1025 kg/m3 .
Answer in units of m.

A stationary ball, with a mass of 0.5 kg, is struck by an identical ball moving at 60m/s . After the collision, the second ball moves 30° to the left of its original direction. The stationary ball moves 60° to the right of the moving ball’s original direction. What is the velocity of each ball after the collision?

A horizontal disk of rotational inertia 7.5 kg m2 with respect to its axis of symmetry is spinning counterclockwise in its plane, about its axis of symmetry at 22.5 revolutions per second. A second disk, of rotational inertia 13.0 kg m2 with respect to its axis of symmetry, spinning clockwise about the same axis (which is also its axis of symmetry) at 20.0 revolutions per second, is dropped on top of the first disk. The two disks stick together and rotate as one about their common axis of symmetry. Determine the new angular velocity of the system.

A centrifuge in the shape of a uniform cylinder of radius 20 cm and mass 10 kg cylinder is spinning about its axis at a speed of 50,000 rpm. Determine the torque that must be applied in order to bring the centrifuge to a stop in 20 s. Calculate the power dissipated.

A block of mass 4.0 kg starts from rest and slides down a surface which corresponds to a quarter of a circle of 2.0 m radius. (i) If the curved surface is smooth, find the speed at the bottom. (ii) If the speed at the bottom is 2.0 ms-1, calculate the energy dissipated due to friction in the descent. (iii) After the block reaches the horizontal with a speed of 2.0 ms-1it slides to a stop in a distance of 1.5 m. Calculate the frictional force acting on the horizontal surface. Take g = 10.0m/s²

A ball of mass kg,.10 starting from rest, falls a height of 4.0 m and then collides with the ground. After the collision, the ball bounces up to a height of 2.0 m. The collision with the ground takes place over a time 4.0 × 10 -³s Determine (i) the momentum of the ball immediately before the collision and immediately after the collision and (ii) the average force exerted by the ground on the ball. Take g = 10.0m/s².

A box of mass 75 kg is placed on an inclined plane. When the angle of the plane is increased to 30º, the box begins to slide downwards. Calculate the coefficient of static friction between the plane and the box. Draw the free body diagram. Take, g = 10.0 ms-²

Consider two simple pendulums P and Q of equal length L and masses m1 and m2 respectively. Suppose the bobs of the pendulum are connected to each other by a weightless spring of force constant k such that in the equilibrium position, the spring is unstretched. Calculate the normal mode frequencies, and draw labelled diagrams corresponding to each mode.