Classical Mechanics Answers

Two masses, one of 2.5 kg and one of 1.5 kg are connected by a light cord passing over a pulley of 150 mm diameter and mass 1 kg, which may be considered as a uniform disc Calculate the acceleration of the masses and the tension in the cord when the system is released from rest.

A vehicle with a mass of 1 500 kg is accelerated with a constant acceleration from rest to a speed of 90 km/h up an incline of 1 in 20. The duration of acceleration is 25 seconds. The constant tractive resistance is 220 N. Calculate:

2.1. The engine power required if the efficiency is 80% at the instant when the vehicle reaches

90 km/h. (8)

2.2. The engine power required to move the vehicle at constant speed of 72 km/h the

efficiency is 82%. (6)

A machine tool has a total mass, m of 150 kg and it is supported on springs with an equivalent stiffness, k = 3375 N/m. Determine:

1.1. The static deflection due to the tool. (1)

1.2. The angular velocity and period of the simple harmonic motion of the tool. (2)

1.3. The amplitude of the simple harmonic motion of the tool if initial conditions are x(0) = 0.08m and v(0) = 0 m/s (4)

1.4. The maximum velocity and maximum acceleration of the motion. (4)

A rigid horizontal bar with weight 16 kN supports three parallel, vertical, straight wires with upper ends firmly secured. The weight of the bar causes the same elongation in each wire. Wire 1 has Area (A)= 20 mm^2 and is made of steel. Wire 2 has Area (A)= 40 mm^2 and is made of copper. Wire 3 is an alloy with Load= 40 kN, elongation of 30 mm over 3 m length. The length of each wire is 3 m. E(Steel)= 200 GPa, E(Copper)= 100 GPa and E(Alloy)= 120 GPa

Calculate the load in each wire and the total elongation?

Two vertically suspended wires are parallel to each other and are also 500 mm apart. The load P carried is W. The first wire is made out of copper and has a diameter of 4 mm. The second wire is made out of steel and has a diameter of 3 mm. The Young's Modulus of Elasticity is 100 GPa for copper and 200 GPa for steel. If the elongation is the same in both wires, calculate the position of W?

• You are given Young's Modulus of Elasticity of 200 GPa and 80 GPa for steel and bronze respectively. Given a cable of steel wire with 4 mm diameter and eight bronze wires of the same size. Find the safe load for the cable and also find the extension under this load on length 43 m. The allowable stress in the bronze wire is 55 MPa. A. 7256.00 N; 29.60 mm
•  B. 7257.08 N; 29.56 mm
•  C. 7256.02 N; 30.10 mm
•  D. 7257.07 N; 30.00 mm

A rigid horizontal bar with weight 16 kN supports three parallel, vertical, straight wires with upper ends firmly secured. The weight of the bar causes the same elongation in each wire. Wire 1 has Area (A)= 20 mm^2 and is made of steel. Wire 2 has Area (A)= 40 mm^2 and is made of copper. Wire 3 is an alloy with Load= 40 kN, elongation of 30 mm over 3 m length. The length of each wire is 3 m. E(Steel)= 200 GPa, E(Copper)= 100 GPa and E(Alloy)= 120 GPa

Calculate the weight of an astronaut whose mass (including spacesuit) is 72 kg on the

Moon. Mass of the Moon = 7.4 × 1022 kg. Radius of Moon = 1.74 × 106 m.

• A rigid horizontal bar with weight 16 kN supports three parallel, vertical, straight wires with upper ends firmly secured. The weight of the bar causes the same elongation in each wire. Wire 1 has Area (A)= 20 mm^2 and is made of steel. Wire 2 has Area (A)= 40 mm^2 and is made of copper. Wire 3 is an alloy with Load= 40 kN, elongation of 30 mm over 3 m length. The length of each wire is 3 m. E(Steel)= 200 GPa, E(Copper)= 100 GPa and E(Alloy)= 120 GPa A. 5.31 kN; 3.98 mm
•  B. 5.33 kN; 4.00 mm
•  C. 5.34 kN; 3.99 mm
•  D. 5.32 kN; 3.99 mm