A spaceship far from all other objects uses its impulse power system to attain a speed of 10⁴ m/s. The crew then shuts off the power. According to Newton's first law, what will happen to the motion of the spaceship from then on? (Select all that apply.)

A ball moves in the direction of the arrow labeled c below. The ball is struck by a stick which briefly exerts a force on the ball in the direction of the arrow labeled e below.

Which arrow best describes the direction of , the change in the ball's momentum?
1 ---Select--- a b c d e f g h j

Field and force with three charges
At a particular moment, one negative and two positive charges are located as shown in Figure 13.46. Your answers to each part of this problem should be vectors. (Let Q₁ = 3 µC, Q₂ = 8 µC, and Q₃ = -5 µC)

Figure 13.46

(a) Find the electric field at the location of Q₁, due to Q₂ and Q₃.
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1,

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2,

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3> N/C
(b) Use the electric field you calculated in part (a) to find the force on Q₁.
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4,

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5,

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6> N
(c) Find the electric field at location A, due to all three charges.
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7,

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8,

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9> N/C
(d) An alpha particle (He²⁺, containing two protons and two neutrons) is released from rest at location A. Use your answer from part (c) to determine the initial acceleration of the alpha particle.
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10,

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11,

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12> m/s²

Relating radius to period for circular orbits
The planets in our Solar System have orbits around the Sun that are nearly circular, and v << c. The period T is one "year", the time required to go around the Sun once. Write a formula for the period T in terms of G, r, and the mass of the Sun M.

Enter a mathematical expression.

1

This is the relationship discovered by Kepler and explained by Newton. (It can be shown by advanced techniques that this result also applies to elliptical orbits if you replace r by the "semimajor axis," which is half the longer, "major" axis of the ellipse.)
Predict the length of a year for Uranus. The mass of the Sun is 2e+30 kg. Uranus has a mass of 8.38e+25 kg and is a distance of 2.87e+12 m from the Sun.

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2 seconds
(You can divide by (365*24*60*60 s) to find how many Earth years this is.)

A spring-like device
A certain spring-like device with uneven windings has the property that to stretch it an amount s from its relaxed length requires a force that is given by F = bs³. You suspend this device vertically, and its unstretched length is 30 cm.

(a) You hang a mass of 21 grams from the device, and you observe that the length is now 36 cm. What is b, including units?
magnitude

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1
units

2

N m     N/m N · m N/m² N · m² N/m³ N · m³

Which of the following were needed in your analysis in part (a)?

3

The fact that the gravitational force acting on an object near the Earth's surface is approximately mg. The momentum principle. The rate of change of momentum being zero. The formula for the period of a spring-mass oscillator.

(c) You hold the 21 gram mass and throw it downward, releasing it when the length of the spring-like device is 40 cm and the speed of the mass is 4 m/s. One millisecond later (where a millisecond is 10^-3 s), what is the stretch of the device, and what is the speed of the mass?
stretch =

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4 m
v =

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5 m/s