Classical Mechanics Answers

Two crossed belts on pulleys of diameters 3.6 m and 2.4 m connect two parallel shafts with centres 4.2 meters apart. The maximum tension in the belts is limited to 1200 N and friction between the belts and the pulley, μ = 0.26. The smaller pulley has a speed of 300 rev/min.

2.1. Find the power that can be transmitted. (8)

2.2. What would be transmitted if open belts were used. (8)

A belt of density of 1500 kg/m^3 and cross-sectional area 400 x 10^-6 m^2 transmits 120 kW power at 1800 rev/min through a pulley of diameter 1.6 m. The angle of lap between the belt and the pulley is 240degrees and μ = 0.2.

Determine:

3.1. The tensions and the maximum stress in the belt. (10)

3.2. The tensions if a grooved pulley with a groove angle of 50degrees . (8)

A plate clutch has two discs on driven shaft, each effective on both sides, and of outer and inner radii 280 mm and 140 mm, respectively. It transmits 45 kN at 2400 rev/min and μ = 0.32 for the friction material. Calculate:

4.1. The axial force needed assuming uniform pressure. (7)

4.2. The force that would be needed assuming uniform wear. (5)

4.3. The maximum power that the belt will transmit. (6)

A cone clutch with cone angle 60degrees , with the same outer inner radii, delivers the same power at the same speed as the clutch in Question 4.

Calculate:

5.1. The cone angle. (8)

5.2. The with width of the clutch. (2)

A locomotive with a mass of 3E5 is accelerating at 0.4m/s2 up an incline of 1 in 20. The rolling resistance is 20 kN of the locomotive. At the instant when the speed of the locomotive is 63 km/h, calculate:

6.1. The power required. (10)

6.2. The kinetic energy of the locomotive. (8)

At what maximum speed can a car safely negotiate a horizontal unbanked turn ( radius = 51m) in dry weather ( coefficient of static friction = 0.95) and icy weather ( coefficient of static friction = 0.10)

A block is placed on top of a fixed smooth inclined plane inclined at 30° to horizontal. The length of plane is 5 m. The block slides down the plane and reaches at bottom. The speed of the block at bottom will be nearly

a particle moves towards a center of attraction starting from rest at a distance a from the centre. if its velocity when at any distance x from the centre varies as √{(a²-x²)/x³} then find the law of force?

Question 2 options:

Given the value for the universal gravitational constant, the average value for the acceleration due to gravity at the surface of Earth, and the radius of Earth, Earth’s mass is ____x10²⁴kg

On a rainy day, a girl broke up with her boyfriend after being together for eight years. They decided to separate at the place where everything about them began, at the same time. The boy is due north crying and running at a rate of 5 ft/sec and the girl is walking due east at rate of 1 ft/sec thinking if she made the right decision. How fast are they separating from each other 5 seconds after they started moving to a new life without each other?

1) Determine the acceleration of a pendulum bob as it passes through an angle of 15 degrees to the right of the equilibrium point.

2) A police car with a siren that has a frequency of 900 Hz is moving toward you at 32.0 m/s. Given that the speed of sound is 340 m/s, what is the apparent frequency you hear?

3) The speed and wavelength of coastal water waves are 4.0 m/s and 6.0 m respectively. When the waves enter a shallower region, the speed decreases to 1.7 m/s. What is the wavelength in the shallower region?

4) The first resonant length of a closed air column occurs when the length is 40 cm. What will the third resonant length be?

5) A pendulum has a mass of 2.35 kg. If the pendulum swings back and forth 110 times in 90.0 seconds, what is the length of the pendulum?

6) A vertical spring is stretched 60.0 cm by a hanging 5.00 kg mass.

a. What is the spring constant?

b. What will be the frequency of vibration of this spring system?