Question

A pair of fuzzy dice is attached to the rearview mirror of a car with a short string. When the car accelerates forward, the string makes an angle of 2.01 degrees from vertical. What is the magnitude of the acceleration, in m/s²

Answer 1

The magnitude of the car's acceleration can be calculated using the angle of the string from vertical, the acceleration due to gravity, and the tangent function. By applying these in the formula associated with Newton's second law, the exact acceleration value can be computed.

Step-by-step explanation:

To determine the magnitude of the acceleration of the car when the fuzzy dice make an angle of 2.01 degrees from vertical, we can use the concept of centripetal acceleration and Newton's second law of motion. Since the only forces acting on the dice in the horizontal direction are due to the car's acceleration, we can say that:

tan(θ) = a/g

Where θ is the angle of the string from vertical (2.01 degrees), a is the acceleration of the car, and g is the acceleration due to gravity, which is approximately 9.81 m/s². We solve for a:

a = g * tan(θ) = 9.81 m/s² * tan(2.01°)

The exact value of a can then be calculated using a calculator.