A car is on a driveway that is inclined 12 degrees to the horizontal. A force of 470lb is required to keep the car from rolling down the driveway.
a) Find the weight of the car
b) Find the force the car exerts against the driveway
To find the weight of the car, we need to understand that weight is the force exerted by an object due to gravity. It can be calculated using the formula: weight = mass × gravitational acceleration.
a) The force required to keep the car from rolling down the inclined driveway is equal to the force that opposes the component of weight acting parallel to the incline. In this case, the force required to keep the car from rolling is 470 lb.
The force component acting parallel to the incline is given by: force parallel = weight × sin(θ),
where θ is the angle of inclination (12 degrees in this case).
Since we're given the force parallel, we can use it to find the weight of the car:
470 lb = weight × sin(12 degrees).
To solve for weight, divide both sides of the equation by sin(12 degrees):
weight = 470 lb ÷ sin(12 degrees).
Now, using a calculator, let's calculate weight:
weight ≈ 1957.796 lb (rounded to the nearest pound).
Therefore, the weight of the car is approximately 1957.796 lb.
b) The force exerted by the car against the driveway can be calculated using the formula: force against = weight × cos(θ).
Using the weight we just calculated and the angle of inclination:
force against = 1957.796 lb × cos(12 degrees).
Using a calculator, let's calculate the force against:
force against ≈ 1923.335 lb (rounded to the nearest pound).
Therefore, the force the car exerts against the driveway is approximately 1923.335 lb.