What is the minimum work needed to push a 900 kg car 890 m up along a 7.5 degree incline?
(a) ignore friction
(b) Assume the effective coefficient of friction retarding the car is 0.20.
a. 1036116.914
b. 2592645.689
To calculate the minimum work needed to push a car up an incline, we need to consider the angle of the incline and the presence or absence of friction.
(a) Ignore friction:
When friction is ignored, the only force we need to overcome is the force due to gravity pulling the car down the incline. The work done against gravity can be calculated using the formula:
Work = Force * Distance * cos(theta)
where
Force = m * g * sin(theta)
m = mass of the car (900 kg)
g = acceleration due to gravity (9.8 m/s^2)
theta = angle of the incline (7.5 degrees)
Plugging the values into the formula, we get:
Force = 900 kg * 9.8 m/s^2 * sin(7.5 degrees)
Distance = 890 m
theta = 7.5 degrees
Work = (900 kg * 9.8 m/s^2 * sin(7.5 degrees)) * 890 m * cos(7.5 degrees)
You can calculate the value of this expression to find the minimum work needed to push the car up the incline without friction.
(b) Assume the effective coefficient of friction retarding the car is 0.20:
In this case, we also need to consider the work done against friction while pushing the car. The force of friction can be calculated using the formula:
Frictional Force = coefficient of friction * normal force
where
coefficient of friction = 0.20
normal force = m * g * cos(theta)
The work done against friction can be calculated using the formula:
Work against friction = Frictional Force * Distance
Plugging in the values, we get:
Frictional Force = 0.20 * (900 kg * 9.8 m/s^2 * cos(7.5 degrees))
Distance = 890 m
Work against friction = (0.20 * (900 kg * 9.8 m/s^2 * cos(7.5 degrees))) * 890 m
To find the minimum work needed to push the car up the incline, we add the work done against gravity (from part (a)) and the work done against friction (from part (b)).
Total work = Work against gravity + Work against friction
You can calculate the values of these expressions and add them to find the minimum work needed to push the car up the incline, taking friction into account.