Respuesta :
Explanation:
a) To balance the mobile, Mrs. Kelly needs to attach the string at the center of mass of the dowel and the ornaments. The center of mass is the point where the torques (rotational forces) from the left and right sides are equal and opposite. To find the center of mass, we can use the formula:
xcm=∑mi∑mixi
where xcm is the position of the center of mass, mi is the mass of each object, and xi is the position of each object relative to a reference point. We can choose any reference point, but for convenience, we can choose the left end of the dowel as the origin. Then, we have:
xcm=0.25+0.11(0.25)(0)+(0.11)(0.75)
xcm=0.41 m
This means that the center of mass is 0.41 m from the left end of the dowel, or 0.34 m from the right end of the dowel. Therefore, Mrs. Kelly needs to attach the string at this point to balance the mobile.
b) To find the tension in the single support string, we can use Newton’s second law for the vertical direction. The net force on the mobile must be zero, since it is not accelerating. The forces acting on the mobile are the tension (T) upward, and the weights of the ornament (W1) and the star (W2) downward. We have:
∑Fy=T−W1−W2=0
T=W1+W2
T=(0.25)(9.8)+(0.11)(9.8)
T=3.53 N
The tension in the single support string is 3.53 N. I hope this helps you understand how to balance a mobile and find the tension in a string. Have a nice day!
