Tractive motion, with gradients, Hard questions

In summary, the conversation discusses the tractive motion of two different vehicles, one being a train and the other a truck. The train has an engine mass of 95 tonnes and is hauling a train of mass 750 tonnes. The tractive resistance to motion for the engine is 120 N/tonne and the rolling resistance for the train is 90 N/tonne. The train initially travels at a speed of 27 km/hr and then accelerates over a distance of 1500m. To achieve this increase in speed, the power required is to be calculated. The train then meets a downgrade of 1V in 110H and is brought to a stop in 900m. The conversation then moves on to discussing
  • #1
paul7776
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tractive motion, with gradients, Hard questions!

4.1 An engine mass of 95 tonnes is hauling a train of mass 750 tonnes along a section of level track. the tractive resistance to motion of the engine is 120 N/tonne and the rolling resistance for the train is 90 N/tonne. initially the engine is traveling at 27 km/hr and then it accelerates over a distance of 1500m.

A) Calculate the power required to achieve this increase in speed?
B)The train then meets a downgrade of 1V in 110H and is brought to a stop in a distance of 900m. calculate the braking force required to stop the train?

4.7 A large truck mass of 35 tonnes is traveling down a gradient of 1V in 60H at a speed of 90 km/hr. The rolling resitance to motion is 115 N tonne.

A) If when the brakes are applied the truck is brought to a stop in 400m what is the applied braking force?
B)How much power is required to provide this braking force?
C)If this same power were available on a uphill gradient of 1 in 60 what constant speed would the truck be capable of reaching?

If u cannot convert km/hr in2 metres per second (ms-1) its (km/hr X 1000) /3600
 
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Welcome to PF!

Hi paul7776! Welcome to PF! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
  • #3


A) To calculate the power required to achieve the increase in speed, we can use the formula P = Fv, where P is power in watts, F is force in newtons, and v is velocity in meters per second. First, we need to convert the initial velocity of 27 km/hr to meters per second by multiplying it by 1000 and dividing by 3600. This gives us a velocity of 7.5 m/s. Then, we can calculate the total tractive resistance to motion by multiplying the engine mass (95 tonnes) by the tractive resistance (120 N/tonne), giving us a force of 11,400 N. The rolling resistance for the train is 90 N/tonne, so we multiply the train mass (750 tonnes) by this resistance, giving us a force of 67,500 N. The total resistance to motion is then 79,900 N. So, the power required to achieve the increase in speed is P = (79,900 N)(7.5 m/s) = 599,250 watts.

B) To calculate the braking force required to stop the train, we can use the formula F = ma, where F is force in newtons, m is mass in kilograms, and a is acceleration in meters per second squared. First, we need to convert the distance of 900m to meters by simply leaving it as 900m. Then, we can calculate the acceleration by dividing the final velocity (0 m/s) by the time it takes to stop (unknown). So, our formula becomes F = (750,000 kg)(0 m/s)/t. We can cancel out the mass and velocity, leaving us with F = 0/t. Since the train is brought to a stop, the time it takes is 0 seconds. This means that the braking force required is 0 newtons.

A) To calculate the applied braking force, we can use the same formula as in part B, F = ma. However, we now have a distance and a final velocity, so we can solve for the acceleration and then use that to find the force. First, we need to convert the speed of 90 km/hr to meters per second by multiplying it by 1000 and dividing by 3600. This gives us a velocity of 25 m/s. Then, we can calculate the acceleration by using the formula a = (vf - vi)/t,
 

1. What is tractive motion?

Tractive motion refers to the movement or displacement of an object or body caused by the application of force or traction.

2. What are gradients in relation to tractive motion?

Gradients, also known as slopes, are changes in elevation or incline along a path or surface. In tractive motion, gradients can affect the amount of force or traction needed to move an object.

3. Can you give an example of a hard question related to tractive motion with gradients?

An example of a hard question related to tractive motion with gradients could be: "How does the gradient of a hill impact the tractive force needed to move a car up the hill?"

4. How do scientists study tractive motion with gradients?

Scientists study tractive motion with gradients by conducting experiments, using mathematical models, and analyzing real-world data to understand the relationship between force, traction, and gradients.

5. Why is understanding tractive motion with gradients important?

Understanding tractive motion with gradients is important in many fields, such as engineering, transportation, and sports. It allows us to design more efficient and effective systems, such as vehicles and equipment, and make informed decisions about how to move objects safely and efficiently in various environments.

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