Question

A 0.0502-kg pair of fuzzy dice is attached to the rearview mirror of a car by a short string. The car accelerates at a constant rate, and the dice hang at an angle of 3.20° from the vertical because of the car’s acceleration. What is the magnitude of the acceleration of the car?

a) 3.25 m/s²
b) 5.80 m/s²
c) 7.15 m/s²
d) 9.40 m/s²

Answer 1

The magnitude of the acceleration of the car is 9.80 m/s², which is the nearest value to the option (d). Hence, it is the correct answer.

Step-by-step explanation:

For this question, we can use the concept of the tension force and the gravitational force to find the magnitude of the car's acceleration. The angle between the string and the vertical is 3.20°, which means there is a component of the tension force acting vertically upwards.

By using trigonometry, we can determine the vertical component of the tension force. The vertical component of the tension force is equal to the gravitational force acting on the dice. Therefore, we can set up the following equation:

Tension force (vertical) = Gravitational force

By using the equation F = ma, where F is the force, m is the mass, and a is the acceleration, we can calculate the magnitude of the car's acceleration.

Using the given data, and assuming that g = 9.8 m/s²:

Tension force (vertical) = m * g

Tension force (vertical) = 0.0502 kg * 9.8 m/s²

Tension force (vertical) = 0.49296 N

The vertical component of the tension force is equal to the gravitational force acting on the dice. Therefore, we can set up the following equation:

Tension force (vertical) = Gravitational force

0.49296 N = m * g

0.49296 N = 0.0502 kg * a

a = 0.49296 N / 0.0502 kg

a = 9.80 m/s²

Therefore, the magnitude of the car's acceleration is 9.80 m/s²