Question

In: Mechanical Engineering

2. A four-wheeled vehicle has a mass of 1500 kg. the tractive resistance is 1100 N....

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]

Expert Solution

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:

samet mamat answered 2 years ago

A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is...

A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is attached to the spring, and the motion takes place in a viscous fluid that offers a resis- tance numerically equal to the magnitude of the instanta- neous velocity. If the system is driven by an external force of (12 cos 3t − 8 sin 3t) N, determine the steady-state response. (a) Find the gain function if the external force is f(t) = cos(ωt). (b)...

An elevator (1500 kg mass, with passengers) is attached to a 1000 kg counterweight by a...

An elevator (1500 kg mass, with passengers) is attached to a 1000 kg counterweight by a cable that is wrapped over a pulley. It is also attached (by a second cable) to a motor. The elevator is moving down at a constant speed of 5 m/s. a) Determine the force that the motor must apply to the second cable. b) Determine the force that the motor must exert to lower the elevator with a constant downward acceleration of 1 m/s^2....

A vehicle (truck A), with a mass of 1800 kg, is tested for safety at a...

A vehicle (truck A), with a mass of 1800 kg, is tested for safety at a lab by having another vehicle (truck B) crash into it from behind. Initially, Truck A is at rest and truck B approaches at about 45 km/hr. After the crash, truck B recoils back at 10 km/hr, while truck A is pushed forward at 27 km/hr. Remember to give all answers in standard units. (This collision would likely be inelastic.) Draw a sketch showing the...

Boxcar #1 has a mass of 2000 kg. Boxcar #2 has a mass of 1200 kg....

Boxcar #1 has a mass of 2000 kg. Boxcar #2 has a mass of 1200 kg. Boxcar #1 is moving at 12.00 m/s to the right before they hit and stick together. A) Suppose that the velocity of Boxcar #2 before the collision is 8.00 m/s to the right. What is the velocity after the totally inelastic collision? B) Suppose, instead, that the speed after the totally inelastic collision is 3.00 m/s. What was the velocity of Boxcar #2 before...

Three cars are approaching an intersection. Car #1 has mass 1500 kg and is driving East...

Three cars are approaching an intersection. Car #1 has mass 1500 kg and is driving East at 10 m/s. Car #2 has mass 2500 kg and is driving North at 20 m/s. Car #3 has mass 2000 kg and is driving South at 30 m/s. a) If the three cars collide simultaneously and stick together, what is their final velocity (magnitude and direction)? b) What fraction of the initial kinetic energy is lost in the collision? c) If the collision...

An automobile having a mass of 1100 kg initially moves along a level highway at 110...

An automobile having a mass of 1100 kg initially moves along a level highway at 110 km/h relative to the highway. It then climbs a hill whose crest is 80 m above the level highway and parks at a rest area located there. Use a reference with kinetic and potential energy each equal to zero for the stationary highway before the hill. Let g = 9.81 m/s2. For the automobile, determine its change in kinetic energy and its change in...

Boxcar #1 has a mass of 2000 kg. Boxcar #2 has a mass of 1200 kg. Boxcar #1...

Boxcar #1 has a mass of 2000 kg. Boxcar #2 has a mass of 1200 kg. Boxcar #1 is moving at 12.00 m/s to the right before they hit and stick together. A) Suppose that the velocity of Boxcar #2 before the collision is 8.00 m/s to the right. What is the velocityafter the totally inelastic collision? B) Suppose, instead, that the speedafter the totally inelastic collision is 3.00 m/s. What was the velocity of Boxcar #2 before the collision? Give all possible answers.

A block of mass 2 kg and a block of mass 3 kg are sliding on...

A block of mass 2 kg and a block of mass 3 kg are sliding on a frictionless surface. They collide and stick together. Before the collision the first block was travelling at 5 m/s in the positive x direction. After the collision the two blocks are travelling at 6 m/s in the negative x direction. What was the x component of the velocity of the second block before the collision?

1)A force of 2 N stretches a spring 0.5 meters. The mass of 1 kg is...

1)A force of 2 N stretches a spring 0.5 meters. The mass of 1 kg is attached to the spring and set into motion in a medium that offers a damped force equal 4 times the velocity. If the mass is at stating from 0.5 m above the equilibrium position with a downward initial velocity of sec/2.0m a) Find the equation for the position if the system is exerted by an external force of f(t)=4cos(t) b)Estimate the position of the...

A spring with a mass of 2 kg has a damping constant 14 kg/s. A force...

A spring with a mass of 2 kg has a damping constant 14 kg/s. A force of 3.6 N is required to keep the spring stretched 0.3 m beyond its natural length. The spring is stretched 0.7 m beyond its natural length and then released. Find the position of the mass at any time t. (Assume that movement to the right is the positive x-direction and the spring is attached to a wall at the left end.) What is x(t)?