Type:
Double
Objective:
Gravitation and Oscillations I & II
Homework: NONE!
Date:_______
AP Physics “B”
Mr. Mirro
Date: ________
Gravitation and Oscillations I
Ex 1: As shown, a physics student observes the Galilean moons of Jupiter over the course of several
nights in order to determine the mass of Jupiter. In doing so, the student only has the equipment
(a timer and a spectrophotometer employing the Doppler Effect) to measure two parameters:
(1) The period of the satellites (moons) and (2) Their orbital velocities.
Callisto
Europa
Io
Ganymede
One orbital revolution of Callisto = 17.0 Earth days [one Earth day = 86 400 sec]
The orbital speed of Callisto = 8,222.0 m/s
a. In order for the student to determine Jupiter’s mass, state what assumptions(s) she must make
about Callisto’s orbit in order to do so.
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b. From the data above, determine the separation distance between the centers of Callisto and
Jupiter.
c. What value of Jupiter’s mass does the student calculate ?
d. If the mass of Earth is 6.0 x 1024 kg, how many times Earth’s mass does the student determine
Jupiter is ?
e. According to her Astronomical Data Tables, the Student determines that her value to part (c)
above, is slightly different than the accepted value for Jupiter’s mass. Calculate the percent
error in her measurement according to your Astronomical Data Tables.
Ex 2: The simple harmonic motion of a 2.0 kg mass oscillating on a spring of elastic constant k is
shown in the sinusoidal graph below.
a. Determine the period of the oscillating mass - ________________
b. Determine the amplitude of the oscillating mass - _____________
The mass is now doubled, and the amplitude and the spring itself are unchanged.
c. Determine the new period of the oscillating mass.
d. Sketch the resulting displacement vs. time graph below.
x (m)
.2
.1
0
t(sec)
.1
.2
e. Write the expression for the resulting displacement from part (d) as a function of time.
f. In each of the cases above, describe clearly the affect on the period of oscillation if the
amplitude of the oscillation is doubled.
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AP Physics “B”
Mr. Mirro
Date: ________
Ex 1: Saturn is the second largest planet in our solar system, having mass and radius that are, 95 and 9.4
times that of earth respectively. Suppose that an object falls from rest near the surface of each
planet and that the acceleration due to gravity remains relatively constant during the fall. Each
object falls the same distance before striking the ground. [CutnellP4.106sim]
a. Develop an expression for ratio of the time of fall on Saturn to that on Earth in terms of the
masses and radii.
b. As an integer, by how much is the time to fall on Saturn shorter than that on Earth ?
c. How long would it take an object to fall 10 m on Saturn ?
d. One of Saturn’s 18 satellites (moons) is in a nearly circular orbit of radius 7 x 109 m, how
many days does it take this satellite to make one complete cycle ? [Recall that ME = 5.98 x 1024 kg]
Ex 2: A projectile is shot straight upward from a giant cannon located near the equator, at sea level on the
surface of the Earth. [Sears12.5sim]
a. Develop the equation for the escape velocity from the surface of the earth in terms of G, ME, RE
and an appropriate constant if necessary.
b. Find the speed that would allow the shell to escape from the earth completely.
[Neglect air resistance, rotation of the earth and gravitational pull of moon]
c. Develop the equation for the muzzle velocity needed to shoot the shell straight up to a height
above the earth equal to the half the earth’s radius in terms of G, ME, RE and an appropriate
constant if necessary.
d. Compute the required muzzle velocity to launch a projectile straight upward to a height that is
half the radius of the Earth.