Question

2. A four-wheeled vehicle has a mass of 1500 kg. the tractive resistance is 1100 N. The engine develops 60 kW at maximum speed of 2500 r/min. The gear ratio is 45:1 and the transmission efficiency is 87.5%. Each wheel has an effective diameter of 800 mm, a mass of 25 kg and a radius of gyration of 325 m
The parts rotating engine speed have a mass of 70 kg and a radius of gyration of 100 mm.
Determine:
a. The acceleration in m/s2 under these condition [0.7034 m/s2]
b. The maximum speed of the vehicle, in km/h [83,78 km/h]

Answer 1

A mistake has been identified according to the given solutions - Gear ratio is 4.5:1 not 45:1

The following parameters are defined:

m - mass of the vehicle

m_e - mass of engine

m_w - mass of wheel

r_e - radius of gyration of engine

r_w - radius of gyration of wheel

r - radius of wheel

eff - efficiency of transmission.

a.:

Equivalent mass of the vehicle that takes into account the effect of rotational components when calculating the acceleration is given by:

Angular speed of the engine is:

Torque available form engine is:

Torque available at the wheels is:

Force at the wheels is:

Total force available for acceleration = 2256.2 - 1100 = 1156.2 N

acceleration = (Total force)/(equivalent mass) = 1156.2/1654.6 = 0.7 m/s².

b.:

Maximum rotational speed of engine = 2500r/min

Maximum rotational speed of wheels = 2500/G = 2500/4.5 = 555.556 r/min = 9.2593 r/sec

Maximum speed of the vehicle v is: