# Mechanics: Problems and Solutions

1. A projectile of mass 0.6 kg is fired vertically upwards in the barrel of a

gun by a vertical net propelling force of 50 N acting over a period of

0.5 seconds.

Calculate:

(a) The velocity of the projectile when it leaves the gun.

(b) The height reached by the projectile.

(c) The time taken from the projectile leaving the gun to its return to the same height.

2. A flywheel (A) with a mass of 100 kg and radius of gyration 1200 mm

rotates at 150 revs min-1 (clockwise). The kinetic energy of this flywheel

is to be reduced by 20% by impacting it with a second flywheel (B)

rotating at 80 revs min-1 in the opposite direction, such that they have the

same (clockwise) angular velocity after impact.

(a) Calculate the required mass of flywheel (B) if its radius of gyration is

800 mm.

(b) Calculate the energy lost to the surroundings.

(c) Is the impact elastic? Give reasons for your answer.

3. A container of mass 100 kg runs on overhead rails. The container is

mounted on two wheels each having a mass of 15 kg, a diameter of 1.2 m

and a radius of gyration of 0.4 m.

Calculate:

(a) The total kinetic energy of the vehicle when travelling at 4 m s-1.

(b) The spring stiffness required to bring the vehicle to rest in a distance

of 300 mm.

4. For a given spring-mass system, what would be the effect on ω of:

(a) Increasing the size of the mass

(b) Increasing the amplitude of vibration

(c) Increasing the spring stiffness

(d) Increasing the phase lag.

5. A mass attached to the lower end of a vertical spring causes the spring to

extend by 25 mm to its equilibrium position. The mass is then displaced

a further 20 mm and released. A trace of the vibration and time

measurements are taken. From these measurements it can be seen that the

displacement from the equilibrium position is 19.2 mm when the time is

0.05 s.

(a) Calculate the expected frequency of vibration.

(b) Calculate the maximum acceleration of the mass.

(c) Calculate the maximum velocity of the mass.

(d) Write the expression for the displacement of the mass as a function of

time.

(e) Write the expression for the velocity of the mass as a function of

time.

(f) Write the expression for the acceleration of the mass as a function of

time.

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#### Solution Summary

This solution is comprised of detailed step-by-step calculations and analysis of the given problems and provides students with a clear perspective of the underlying concepts.

Various Physics (Mechanics) Problems

(See attached file for full problem description)

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37. A block whose weight is 45.0 N rests on a horizontal table. A horizontal force of 36.0 N is applied to the block. The coefficients of static and kinetic friction are 0.650 and 0.420, respectively. Will the block move under the influence of the force, and, if so, what will be the block's acceleration? Explain your reasoning.

47. A supertanker (mass = 1.70 X 108 kg) is moving with a constant velocity. Its engines generate a forward thrust of 7.40 X 105 N. Determine (a) the magnitude of the resistive force exerted on the tanker by the water and (b) the magnitude of the upward buoyant force exerted on the tanker by the water.

51. A stuntman is being pulled along a rough road at a constant velocity, by a cable attached to a moving truck. The cable is parallel to the ground. The mass of the stuntman is 109 kg, and the coefficient of kinetic friction between the road and him is 0.870. Find the tension in the cable.

63. Only two forces act on an object (mass = 4.00 kg), as in the drawing. Find the magnitude and direction (relative to the x axis) of the acceleration of the object.

67. In the drawing, the weight of the block on the table is 422 N and that of the hanging block is 185 N. Ignoring all frictional effects and assuming the pulley to be massless, find (a) the acceleration of the two blocks and (b) the tension in the cord.

73. A 1.14 X 104-kg lunar landing craft is about to touch down on the surface of the moon, where the acceleration due to gravity is 1.60 m/s2. At an altitude of 165 m the craft's downward velocity is 18.0 m/s. To slow down the craft, a retrorocket is firing to provide an upward thrust. Assuming the descent is vertical, find the magnitude of the thrust needed to reduce the velocity to zero at the instant when the craft touches the lunar surface.

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