What is the minimum work in joules needed to push a 1840 kg car 14.0 m up a 12.5 degree incline? (Ignore friction.)
Wc = m*g = 1840kg * 9.8N/kg = 18032 N. =
Wt. of car.
Fc = 18,032N[12.5o] = Force of the car.
Fp = 18,032*sin12.5 = 3903 N. = Force
parallel to incline.
F-Fp = m*a = m*0 = 0
F-3903 = 0
F = 3903 N. Parallel to the incline
Work = F*d = 3903 * 14 = 54,642 J.
To calculate the minimum work in joules needed to push the car up the incline, we need to use the formula:
Work = Force × Distance × cos(θ)
First, let's calculate the force required to move the car up the incline. The force can be calculated using the formula:
Force = Mass × Acceleration
Since the car is on an inclined plane, we need to decompose the force into two components: one parallel to the incline and one perpendicular to the incline.
The force parallel to the incline can be calculated as:
Force_parallel = Mass × Acceleration_parallel
The acceleration parallel to the incline can be calculated using the formula:
Acceleration_parallel = Acceleration_due_to_gravity × sin(θ)
The acceleration due to gravity is a constant, which is approximately 9.8 m/s^2.
Now, let's calculate the force parallel to the incline:
Force_parallel = Mass × Acceleration_due_to_gravity × sin(θ)
Given:
Mass of car (m) = 1840 kg
Angle of incline (θ) = 12.5 degrees
Acceleration_parallel = 9.8 m/s^2 × sin(12.5°)
Next, let's calculate the distance covered (d) in meters:
Distance (d) = 14.0 m
Now, we can calculate the minimum work required:
Work = Force_parallel × Distance × cos(θ)
Work = (Mass × Acceleration_due_to_gravity × sin(θ)) × Distance × cos(θ)
Substituting the given values, we get:
Work = (1840 kg × 9.8 m/s^2 × sin(12.5°)) × 14.0 m × cos(12.5°)
Calculating the expression, we get:
Work ≈ 196,941.3 J
Therefore, the minimum work required to push the 1840 kg car 14.0 m up the 12.5 degree incline (ignoring friction) is approximately 196,941.3 Joules.
To calculate the minimum work needed to push the car up the incline, we need to consider the gravitational potential energy gained by the car.
The gravitational potential energy (PE) gained by an object when it is raised to a certain height is given by the equation:
PE = m * g * h
Where:
m = mass of the object
g = acceleration due to gravity (approximately 9.8 m/s^2 on Earth)
h = height or vertical distance
In this case, the car is being pushed up an incline of 12.5 degrees, which means the height (h) can be calculated using trigonometry. We can use the formula:
h = d * sin(theta)
Where:
d = horizontal distance
theta = angle of incline
In this case, the horizontal distance (d) is given as 14.0 m and the angle of incline (theta) is given as 12.5 degrees. So we can calculate the height (h) using the formula.