A dumbbell has a mass m on either end of a rod of length 2 a . The center of the dumbbell is a distance r from the center of the Earth, and the dumbbell is aligned radially. If r ≫ a , show that the difference in the gravitational force exerted on the two masses by the earth is approximately 4 GmM E a / r 3 . ( Note: The difference in force causes a tension in the rod connecting the masses. We refer to this as a tidal force .) [ Hint: Use the fact that 1/( r − a ) 2 − 1/( r + a ) 2 ~ 4 a / r 3 for r ≫ a .]
A dumbbell has a mass m on either end of a rod of length 2 a . The center of the dumbbell is a distance r from the center of the Earth, and the dumbbell is aligned radially. If r ≫ a , show that the difference in the gravitational force exerted on the two masses by the earth is approximately 4 GmM E a / r 3 . ( Note: The difference in force causes a tension in the rod connecting the masses. We refer to this as a tidal force .) [ Hint: Use the fact that 1/( r − a ) 2 − 1/( r + a ) 2 ~ 4 a / r 3 for r ≫ a .]
A dumbbell has a mass m on either end of a rod of length 2a. The center of the dumbbell is a distance r from the center of the Earth, and the dumbbell is aligned radially. If r ≫ a, show that the difference in the gravitational force exerted on the two masses by the earth is approximately 4GmMEa/r3. (Note: The difference in force causes a tension in the rod connecting the masses. We refer to this as a tidal force.) [Hint: Use the fact that 1/(r − a)2 − 1/(r + a)2 ~ 4a/r3 for r ≫ a.]
2. A projectile is shot from a launcher at an angle 0,, with an initial velocity
magnitude vo, from a point even with a tabletop. The projectile hits an apple atop a
child's noggin (see Figure 1). The apple is a height y above the tabletop, and a
horizontal distance x from the launcher. Set this up as a formal problem, and solve
for x. That is, determine an expression for x in terms of only v₁, 0, y and g.
Actually, this is quite a long expression. So, if you want, you can determine an
expression for x in terms of v., 0., and time t, and determine another expression for
timet (in terms of v., 0.,y and g) that you will solve and then substitute the value of
t into the expression for x. Your final equation(s) will be called Equation 3 (and
Equation 4).
Draw a phase portrait for an oscillating, damped spring.
A person is running a temperature of 41.0°C. What is the equivalent temperature on the Fahrenheit scale? (Enter your answer to at least three significant figures.)
°F
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