A car of mass 1500 kg accelerates up a hill of incline 8 degrees, increasing its speed from 4 ms to 16 ms over a distance of 90m. Assuming a total frictional resistance of 1000 N, calculte:
a) the tractive effort between the wheels and the road surface
b)the work done during the period of acceleration
c)the average power developed
To calculate the required values in this problem, we need to use some basic physics equations and principles. Here's how you can obtain the answers to each part of the question:
a) The tractive effort between the wheels and the road surface can be calculated using the equation:
Tractive effort = Total force - Frictional resistance
Total force = mass x acceleration
First, we need to calculate the acceleration of the car. We can use the following kinematic equation:
v^2 = u^2 + 2as
where,
v = final velocity = 16 m/s
u = initial velocity = 4 m/s
s = distance = 90 m
Rearranging the equation and solving for acceleration (a):
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = (16^2 - 4^2) / (2 x 90)
= 248 / 180
= 1.3778 m/s^2
Now, let's calculate the tractive effort:
Total force = mass x acceleration
= 1500 kg x 1.3778 m/s^2
Frictional resistance = 1000 N
Tractive effort = Total force - Frictional resistance
b) The work done during the period of acceleration can be calculated using the work-energy principle. The work done is equal to the change in kinetic energy:
Work done = Change in kinetic energy = (1/2) x mass x (final velocity^2 - initial velocity^2)
Substituting the given values:
Work done = (1/2) x 1500 kg x (16^2 - 4^2)
c) The average power developed can be calculated by using the formula:
Average power = Work done / time
To calculate the time, we can use the formula:
time = Distance / average velocity
Average velocity = (initial velocity + final velocity) / 2
Substituting the given values:
Average power = Work done / time
Now, you have the steps to solve all three parts of the question. Just substitute the values into the equations, and you will get the answers.