. A space craft achieved a maximum speed of 125,000 km/h on its way to photograph Mars. Beyond what distance from the Sun is this speed sufficient to escape the solar system? Explain your calculation.

. A space craft achieved a maximum speed of 125,000 km/h on its way to photograph Mars. Beyond what distance from the Sun is this speed sufficient to escape the solar system? Explain your calculation.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter7: Gravity

Section: Chapter Questions

Problem 7PQ: Model the Moons orbit around the Earth as an ellipse with the Earth at one focus. The Moons farthest...

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Question

Known values
Mass of Sun: 1.99×1030 kg; Mass of Earth: 5.98×10²* kg; Mass of Moon: 7.36×10²² kg;
Earth-Sun distance = 1,50×10" m; Mars-Sun distance = 2.48 × 10" m; Earth-Moon distance = 3.82×10* m; Radius
%3D
of Earth: 6380 km; Moment of inertia: solid sphere rotating about diameter- I =
MR2; Damped harmonic motion
function: x(t) = xoe™
t/2f cos(w't + w); t =;w' = wo [1 - (
–)²; wo =.
2mwo'
%3D
m
Question 3
A space craft achieved a maximum speed of 125,000 km/h on its way to photograph Mars. Beyond
what distance from the Sun is this speed sufficient to escape the solar system? Explain your
а.
calculation.
b. Two uniform spheres, each of mass 0.260 kg, are fixed at points A and B (Figure). Find the
magnitude and direction of the initial acceleration of a uniform sphere with mass 0.010 kg if
released from rest at point P and acted on only by forces of gravitational attraction of the spheres
at A and B.
0.010 kg
10.0 cm 10.0 cm
0.260 kg 6.0 cm0.260 kg
8.0 cm | 8.0 cm
BE
Figure 2: Question 3(b) Two masses system

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Known values Mass of Sun: 1.99×103º kg; Mass of Earth: 5.98×10²4 kg; Mass of Moon: 7.36×10²² kg; Earth-Sun distance = 1.50×10" m; Mars-Sun distance = 2.48×10'" m; Earth-Moon distance = 3.82×10° m; Radius of Earth: 6380 km; Moment of inertia: solid sphere rotating about diameter- I = - MR²; Damped harmonic motion k function: x(t) = xge "{/2" cos(w't + q); t = ;w' = w, 1-; wo 2mwo' Question 5 a. Explain why you expect an object made of a stiff material to vibrate at a higher frequency than a similar object made of a more flexible material. Figure 3: Question 5(a) Samples of stiff and flexible material b. Consider a large massive spherical shell object. With all of its mass M is distributed at its radius R (shown in the figure). Draw a schematic graph of gravitational force and corresponding gravitational potential energy experienced by another object m at a distance r, where the distance varies as, r → 0 to r → ∞. Justify your answer. Figure 4: Question 5(a) Two masses system
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Known values Mass of Sun: 1.99×1030 kg; Mass of Earth: 5.98×10²4 kg; Mass of Moon: 7.36×10²² kg; Earth-Sun distance = 1.50×10" m; Mars-Sun distance = 2.48×10'' m; Earth-Moon distance = 3.82×10$ m; Radius of Earth: 6380 km; Moment of inertia: solid sphere rotating about diameter- I = -MR²; Damped harmonic motion %3D m b function: x(t) = x,e¬t/2t cos(w't + ø); t = ";w' = wo.[1 – -)2; wo = 2mwo b b. Two uniform spheres, each of mass 0.260 kg, are fixed at points A and B (Figure). Find the magnitude and direction of the initial acceleration of a uniform sphere with mass 0.010 kg if released from rest at point P and acted on only by forces of gravitational attraction of the spheres at A and B. 0,010 kg PO 10.0 cm 10.0 cm 0.260 kg - 6.0 cm` 0.260 kg 8.0 cm | 8.0 cm A В Figure 2: Question 3(b) Two masses system