(a) Find the escape speed of a projectile from the surface of the Moon. (See the front of the test for some numbers you may need here.) (b) Imagine you want to launch a package of mass 3kg from the surface of the Moon in such a way that it will never come back, and when it is very far from the Moon it will still be traveling with a speed of 50 m/s. You have a large and powerful spring whose stiffness is 6 x 10° N/m. How much do you have to compress the spring?

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Chapter1: Units, Trigonometry. And Vectors
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(a) Find the escape speed of a projectile from the surface of the Moon. (See the front of the
test for some numbers you may need here.)
(b) Imagine you want to launch a package of mass 3kg from the surface of the Moon in such
a way that it will never come back, and when it is very far from the Moon it will still be
traveling with a speed of 50 m/s. You have a large and powerful spring whose stiffness is
6 × 10 N/m. How much do you have to compress the spring?
Transcribed Image Text:(a) Find the escape speed of a projectile from the surface of the Moon. (See the front of the test for some numbers you may need here.) (b) Imagine you want to launch a package of mass 3kg from the surface of the Moon in such a way that it will never come back, and when it is very far from the Moon it will still be traveling with a speed of 50 m/s. You have a large and powerful spring whose stiffness is 6 × 10 N/m. How much do you have to compress the spring?
Constants and other possibly useful numbers
g = 9.8m/s?
G = 6.67 × 10-11 Nm/kg?
c= 3 x 10°m/s
Radius of the Moon: 1.74 x 106m
Mass of the Sun: 2 x 1030kg
Radius of the Sun: 6.957 x 10°m
Mass of an electron me =9.11 x 10-31kg
Mass of a proton mp
1.67 x 10-27kg
%3D
Average distance between the Moon and Earth:
3.84 x 10 m
Average distance between Sun and Earth: 1.5 x
1011m
Mass of Earth: 6 x 1024kg
Radius of Earth: 6.4 x 106m
Mass of the Moon: 7.35 x 1022kg
Moments of Inertia:
R+ R
2.
MR²
1
2
I =Em;r? Iring = M
Idisk =ML Igphere =M R
= Icylinder =MR Irod
I disk
%3D
%D
%3D
12
The vector product or cross product between two vectors A and B can be calculated as follows:
If you know the angle 0 between the two vectors, find the magnitude of the product |C| = |Ã × B| =
|A||B| sin 0 and find the direction using the right-hand-rule.
%3D
Transcribed Image Text:Constants and other possibly useful numbers g = 9.8m/s? G = 6.67 × 10-11 Nm/kg? c= 3 x 10°m/s Radius of the Moon: 1.74 x 106m Mass of the Sun: 2 x 1030kg Radius of the Sun: 6.957 x 10°m Mass of an electron me =9.11 x 10-31kg Mass of a proton mp 1.67 x 10-27kg %3D Average distance between the Moon and Earth: 3.84 x 10 m Average distance between Sun and Earth: 1.5 x 1011m Mass of Earth: 6 x 1024kg Radius of Earth: 6.4 x 106m Mass of the Moon: 7.35 x 1022kg Moments of Inertia: R+ R 2. MR² 1 2 I =Em;r? Iring = M Idisk =ML Igphere =M R = Icylinder =MR Irod I disk %3D %D %3D 12 The vector product or cross product between two vectors A and B can be calculated as follows: If you know the angle 0 between the two vectors, find the magnitude of the product |C| = |Ã × B| = |A||B| sin 0 and find the direction using the right-hand-rule. %3D
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