What is the minimum work in joules needed to push a 1540 kg car 44.0 m up a 12.5 degree incline?
M*g*H, where H is the vertical rise, 44 sin12.5 meters.
g = 9.8 m/s^2
The answer will be in Joules.
To find the minimum work needed to push the car up the incline, we can use the formula:
Work = Force × Distance × Cos(θ)
Where:
- Force is the force applied to push the car uphill.
- Distance is the distance the car is moved uphill.
- θ is the angle of the incline.
First, we need to find the force applied to push the car uphill. The force can be calculated using the formula:
Force = Weight × sin(θ)
Where:
- Weight is the weight of the car, given by the formula: Weight = mass × gravitational acceleration (g)
The gravitational acceleration is approximately 9.8 m/s^2.
Weight = mass × g = 1540 kg × 9.8 m/s^2 = 15092 N
Now, we can calculate the force:
Force = Weight × sin(θ) = 15092 N × sin(12.5°) = 3289.7 N
Next, we can calculate the work:
Work = Force × Distance × Cos(θ) = 3289.7 N × 44.0 m × cos(12.5°)
Now, let's plug in the values and calculate the minimum work needed to push the car uphill.