Your friend's 11.1g tassel hangs on a string from his rear-view mirror. When he accelerates from a stop light, the tassel deflects backward toward the rear of the car. If the tassel hangs at an angle of 6.89deg relative to the vertical, what is the acceleration of the car?

From the ratio of horizontal to vertical forces on the tassel:

M*a = M*g tan6.89

M cancels out.

Solve for a.

To find the acceleration of the car, we can use Newton's second law of motion, which states that the net force on an object is equal to its mass multiplied by its acceleration (F = m * a).

In this case, the force acting on the tassel is the force due to gravity, since it is hanging vertically. The weight of the tassel can be calculated using the equation: weight = mass * gravitational acceleration, where the gravitational acceleration is approximately 9.8 m/s^2.

The weight of the tassel is given by:
weight = (11.1 g) * (9.8 m/s^2)
weight = 0.0111 kg * 9.8 m/s^2
weight ≈ 0.109 kg * m/s^2

Now, we need to determine the net force on the tassel in the horizontal direction. The net force is the component of the weight force acting in the horizontal direction, which can be found by multiplying the weight by the sine of the angle between the vertical and the direction of acceleration.

Net force (horizontal) = weight * sin(angle)
Net force (horizontal) = 0.109 kg * m/s^2 * sin(6.89°)

Now, since the tassel deflects backward toward the rear of the car, the horizontal net force is also equal to the mass of the tassel multiplied by the acceleration of the car.

Therefore, we can equate the two expressions for the net force:
Net force (horizontal) = m * a

0.109 kg * m/s^2 * sin(6.89°) = (11.1 g) * a

Here, we need to convert the mass of the tassel from grams to kilograms:
m = 11.1 g = 0.0111 kg

Plugging in the values, we have:
0.109 kg * m/s^2 * sin(6.89°) = (0.0111 kg) * a

Simplifying, we get:
0.109 * sin(6.89°) = a

Calculating the right side of the equation:
a ≈ 0.109 * sin(6.89°)
a ≈ 0.012 m/s^2

Thus, the acceleration of the car is approximately 0.012 m/s^2.