Physics HW?

Question

Objects that are at rest relative to Earth's surface are in circular motion due to Earth's rotation. What is the centripetal acceleration of an object in a town in Europe, at a latitude of 39 deg North?

a)0.0262 m/s2
b)0.0218 m/s2
c)0.0377 m/s2
d)0.0314 m/s2

The answer is either a, b, c, or d. I've looked in the book for an equation to help me solve this, but I can't manage to find one that seems to work for this problem. Any Ideas on how to get the answer?? like what equation to use??

Thanks so much!

Answer 1

As I'm sure you know, centripetal force is represented by:


F = m(v^2/r)

Where m is the mass, v^2 is the velocity and r is the radius.

Since earth is a sphere, the widest point is at the equator. You will have a different velocity since the circumference is smaller at 39 degrees North. You also need the object's mass.

The radius of the earth is, according to Google, 6,378.1 km
Multiply by 1,000 to get the units in meters. (We'll do that later)

Now, on to velocity. But first, let's get a distance traveled...or the circumference of the Earth at 39 degrees. The formula will be:

C = 2 pi r cos(x)

Where r is the equatorial radius and x is the angle of latitude.

This works out to be:

2 (3.14) (6,378) cos (39) or--31128.1 km

Good ol' rate x time now...

R x T = D

R is unknown, time is 24 hrs = Distance

r(24)=31128.1

r = 1297 km/hr

Back to our original formula:


F=mv^2/r

Take your mass, plug away, and don't forget to convert your units from km/hr!

Good luck!

Mysstere

Answer 2

Acceleration = tension / mass. speed = acceleration * time. potential = tension * speed #a million assume uniform tension at each and every section. in the blocks, the acceleration = 5/0.2 = 20m/s² tension = 20*70 = a million,400N Out of the blocks, acceleration = (12-5)/5 = 7/5m/s² tension = 7/5*70 = 98N general potential = ninety 8*(12+5)/2 = 833W #2 Conservation of potential. assume gravity = 10 m/s² (you ought to use 9.80 one in case you like and you have a calculator) potential potential at 100m relative to the floor = 10 * a hundred * 3 = 3,000J potential potential at 50m = a million,500J Kinetic potential at 50m = a million,500J you are able to calculate its speed from this: 31.6 m/s