Physics 1 difficult question,Comes from resistive force chapter? NEED HELP ASAP TONIGHT?

Question

A plumb bob does not hang exactly along a line directed to the center of the Earth's rotation. How much does the plumb bob deviate from a radial line at 32.5° north latitude? Assume that the Earth is spherical.

answer is wanted in degrees


HAVE THIS MUCH SO FAR from someone who answered.

The acceleration from the earth's rotation at 32.5° lat is
a = Re*cos32.5°*ω² = 2.84E-5 m/s²
Combining that with g at Lat 32.5 gives a deviation of roughly 8.93E-5°. The deviation will be toward the equator.

Draw a diagram with 9.8 m/s² acting toward the center and the value of a above acting outward perpendicular to the axis of the earth. This will give you a triangle with 2 sides and one angle known.

The tilt of the earth's axis doesn't enter into the answer.....

still do not understand how the deviation he listed will help me in figuring out the last side of the triangle.

A plumb bob does not hang exactly along a line directed to the center of the Earth's rotation. How much does the plumb bob deviate from a radial line at 32.5° north latitude? Assume that the Earth is spherical.

answer is wanted in degrees


HAVE THIS MUCH SO FAR from someone who answered.

The acceleration from the earth's rotation at 32.5° lat is
a = Re*cos32.5°*ω² = 2.84E-5 m/s²
Combining that with g at Lat 32.5 gives a deviation of roughly 8.93E-5°. The deviation will be toward the equator.

Draw a diagram with 9.8 m/s² acting toward the center and the value of a above acting outward perpendicular to the axis of the earth. This will give you a triangle with 2 sides and one angle known.

The tilt of the earth's axis doesn't enter into the answer.

.so i drew a triangle with the x axis equaling 2.84e-5, and the y-axis is just 9.8m/s from what i understood? the vector line goes in the direction of up and to the right in between the x and y axis. what angle do i need?

Answer 1

You don't need the magnitude of the third side, you need its angle.

Let's assume the center of the earth is the origin for the vector triangle, with the earth's axis of rotation along the vertical axis (the y axis). You have a line of magnitude 9.8 m/s² extending upwards, lets say to the right, at an angle of 32.5°. The vector (the arrowhead) points towards the origin since gravity is pulling towards the center of the earth.

The base of the triangle is a line of magnitude 2.84E-5 m/s² extending from the center to the right representing the centripetal acceleration on the bob. Centripetal acceleration tends to throw things radially away from the rotation axis, that is, perpendicular to the axis of the earth (in the direction of the x axis).

The third side, connecting the ends of the two lines, represents the net acceleration on the bob. Since it is the vector sum of the other two, the arrow points from the "tail" of the long (gravity) line to the "head" of the short (centripetal) line. The angle between the two long sides (gravitational acceleration and net acceleration) gives you your 8.93E-5°. Or at least I presume it does; I did not actually check the value.

Answer 2

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Answer 3

SAS-side angle side would be one approach