A vintage sports car accelerates down a slope of θ = 16.6°. The driver notices that the strings of the fuzzy dice hanging from his rear-view mirror are perpendicular with respect to the roof of the car. What is the acceleration of the car?
To find the acceleration of the car, we need to break down the forces acting on it. In this case, we have the force of gravity acting vertically downward and the force of the car's acceleration acting along the slope of the hill.
The force of gravity can be broken down into two components: one parallel to the slope and one perpendicular to the slope. The component of gravity perpendicular to the slope is equal to mg * cos(θ), where m is the mass of the car and g is the acceleration due to gravity.
The force of the car's acceleration can also be broken down into two components: one parallel to the slope and one perpendicular to the slope. Since the driver notices that the strings of the fuzzy dice hanging from his rear-view mirror are perpendicular to the roof of the car, we can conclude that the car's acceleration component perpendicular to the slope must be equal to the component of gravity perpendicular to the slope.
Therefore, the acceleration of the car can be calculated using the formula:
acceleration = force / mass
Since the component of the car's acceleration perpendicular to the slope is equal to the component of gravity perpendicular to the slope, we can substitute mg * cos(θ) for force:
acceleration = (mg * cos(θ)) / m
The mass cancels out, leaving us with:
acceleration = g * cos(θ)
Now, we can plug in the values:
θ = 16.6° (slope angle)
g = 9.8 m/s² (acceleration due to gravity)
acceleration = 9.8 m/s² * cos(16.6°)
Using a calculator, we can find the cosine of 16.6° as 0.9606:
acceleration ≈ 9.8 m/s² * 0.9606 ≈ 9.41 m/s²
Therefore, the acceleration of the car is approximately 9.41 m/s².