What is the minimum work in joules needed to push a 1460 kg car 14.0 m up a 12.5 degree incline? (Ignore friction.)

Work required = Gain in PE

= m*g*h
= 1460*9.8*14Sin12.5 J
(h-vertical height gained)

To calculate the minimum work needed to push the car up the incline, we can use the formula:

Work = Force × Distance

To determine the force required, we need to consider the component of the car's weight that acts parallel to the incline. We can do this by calculating the weight of the car and then finding its parallel component.

Step 1: Calculate the weight of the car:
The weight of an object is given by the formula:
Weight = Mass × Gravity

The mass of the car is provided as 1460 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.

Weight = 1460 kg × 9.8 m/s^2

Step 2: Find the parallel component of the weight:
The parallel component of the weight is equal to the weight times the sine of the angle of the incline.

Parallel Component = Weight × sin(θ)

Here, θ is the angle of the incline, which is given as 12.5 degrees.

Parallel Component = Weight × sin(12.5 degrees)

Step 3: Calculate the work done:
Now, we can calculate the work done by multiplying the parallel component of the weight by the distance the car is pushed up the incline.

Work = Parallel Component × Distance

Distance is given as 14.0 m.

Work = Parallel Component × 14.0 m

Finally, we can substitute the value of the parallel component into the equation to calculate the minimum work needed to push the car up the incline.