Question

Dana has a sports medal suspended by a long ribbon from her rearview mirror. as she accelerates onto the highway, she notices that the medal is hanging at an angle of 15 â from the vertical. part a does the medal lean toward or away from the windshield? does the medal lean toward or away from the windshield? away from the windshield toward the windshield submitmy answersgive up correct part b what is her acceleration?

Answer 1

When Dana accelerates onto the highway, the sports medal leans away from the windshield due to inertia. Dana's acceleration is approximately 2.51 m/s^2 away from the wall.

Step-by-step explanation:

When Dana accelerates onto the highway, the sports medal suspended from her rearview mirror leans away from the windshield. This can be attributed to the inertia of the medal. As the car accelerates, the medal tends to remain at rest due to inertia while the car moves forward. Thus, the medal appears to lean away from the windshield.

To find Dana's acceleration, we can use the given information that the medal hangs at an angle of 15 degrees from the vertical. The acceleration can be calculated using the equation:

acceleration = g * tan(angle)

Substituting the given values, we get:

acceleration = 9.8 m/s^2 * tan(15 degrees)

Therefore, Dana's acceleration is approximately 2.51 m/s^2 away from the wall.

Answer 2

Refer to the diagram shown below.

m = the mass of the medal
T = the tension in the string
g = 9.8 m/s²

Part (a)
The inertial force, F, tends to move the medal away from the windshield when the vehicle accelerates to the right.

Answer: The medal leans away from the windshield.

Part (b)
For force balance,
T cos(15°) = mg
0.9659 T = 9.8m
T = 10.1457m N

Also,
F = Tsin(15°) = 10.1457m*0.2588 = 2.6257m N
The inertial force is equal to the accelerating force, therefore
the acceleration, a, is given by
(2.6257m N) = (m kg)*(a m/s²)
a = 2.6257 m/s²

Answer: 2.626 m/s²