A 3000 pound car sits on a hill, which is at an incline of 30°. Assuming there is no friction, what force is required to keep the car from rolling down the hill? (Type your numerical answer in the box below without any units)
Question
A 3000 pound car sits on a hill, which is at an incline of 30°. Assuming there is no friction, what force is required to keep the car from rolling down the hill? (Type your numerical answer in the box below without any units)
Solution
To find the force required to keep the car from rolling down the hill, we need to calculate the component of the car's weight that acts parallel to the hill. This is given by the formula:
F = m * g * sin(θ)
where:
- m is the mass of the car,
- g is the acceleration due to gravity, and
- θ is the angle of the hill.
First, we need to convert the weight of the car to mass. Since the weight is given in pounds, we know that 1 pound is approximately equal to 0.453592 kg. So, the mass of the car is:
m = 3000 pounds * 0.453592 kg/pound = 1360.78 kg
Next, we know that the acceleration due to gravity is approximately 9.8 m/s².
Finally, the angle of the hill is given as 30°.
Substituting these values into the formula gives:
F = 1360.78 kg * 9.8 m/s² * sin(30°) = 6668.63 Newtons
So, the force required to keep the car from rolling down the hill is approximately 6668.63 Newtons.
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