Escape velocity and black holes The work required to launch an object from the surface of Earth to outer space is given by w = JEF(x) dx, where R = 6370 km is the approximate radius is the gravitational force between Earth and the object, G is the gravitational constant, M is the mass of Earth, m is the mass of the object, and GM = 4 x 1014 m²/s?. GMm of Earth, F(x) = x? a. Find the work required to launch an object in terms of m. b. What escape velocity v, is required to give the object a kinetic 1 energy mv? equal to W? c. The French scientist Laplace anticipated the existence of black holes in the 18th century with the following argument: If a body has an escape velocity that equals or exceeds the speed of light, c = 300,000 km/s, then light cannot escape the body and it cannot be seen. Show that such a body has a radius Rs 2GM/c. For Earth to be a black hole, what would its radius need to be?

How to find Kinetic Energy?  KE= 1/2mv1 2   m= 60 grams      v1= 688.75

1 2. Preparations are under way for a spacecraft visit to the Alpha Centauri star system, 4.30- lightyears away Provisions are placed on board to allow for a trip of 8 years. a. What minimum speed must the spacecraft travel relative to Earth if the provisions are to last?

where did the 1.602 X10^-19 come from?

A star is 16.6 light-years from Earth. Part A How long would it take a spacecraft traveling 0.950c to reach that star as measured by observer on Earth? tEarth = 53.25 Submit Previous Answers Request Answer Part B X Incorrect; Try Again; 4 attempts remaining t = 175| ΑΣΦ Submit Part C How long would it take a spacecraft traveling 0.950c to reach that star as measured by observer on the spacecraft? 1 = 15. ΑΣΦ Submit 5 Request Answer [ΠΙ ΑΣΦ www F Request Answer 2 ? What is the distance traveled according to observers on the spacecraft? ? years ? years light-years

1. Read and U What information are you given? Mass= m = 0.15 kg Speed of light = c = 300,000,000 m/s = 3 x 108 m/s 2. Plan and Solve What unknown are you trying to calculate? The amount of energy produced = E = ? What formula contains the given quantities and the unknown? E = mc2 Replace each variable with its known variable and known value. E = (0.15 kg)(3.00 x 108 m/s)2 E = 1.35 x 10¹6 kg.m²/s2 = 1.4 x 1016 J 3. Look Back and Check a separate In a nuclear reactor, 1.5 kilograms of plutonium-239 is completely converted to energy. How many joules of energy are produced? nits

A star is 16.6 light-years from Earth. Part A How long would it take a spacecraft traveling 0.950c to reach that star as measured by observer on Earth? tEarth 17.5 years Submit ✓ Part B Correct How long would it take a spacecraft traveling 0.950c to reach that star as measured by observer on the spacecraft? t = 5.46 years Submit ✓ Previous Answers Part C Correct Submit What is the distance traveled according to observers on the spacecraft? 15.18 light-years Previous Answers Part D Correct Previous Answers v= 5.18 What will the spacecraft occupants compute their speed to be from the results of part B and part C? IT| ΑΣΦ Submit Previous Answers Request Answer ? X Incorrect; Try Again; 3 attempts remaining .C

What is proper time? A. The time calculated for the person moving at relativistic speed. B. The longest possible time interval between two events. C. The time measured by the clock that travels with the observer. D. The time measured by a light clock.

1. If a subatomic particle moves close to the speed of light. Its decay would occur ___? 2.  A space explorer travels between asteroids that are 100 000 m apart. His/her space probe travels with constant speed of 0.8c=2.4x108 m/s. What is the time of the trip between asteroids measured by observer on one of the asteroids? Write your answer rounded to 2 decimal places in ms

A star is 16.6 light-years from Earth. Part A How long would it take a spacecraft traveling 0.950c to reach that star as measured by observer on Earth? tEarth 17.5 years Submit ✓ Correct Correct answer is shown. Your answer 17.47 years was either rounded differently or used a different number of significant figures than required for this part. Part B How long would it take a spacecraft traveling 0.950c to reach that star as measured by observer on the spacecraft? t = 5.46 years Submit Part C Previous Answers Correct What is the distance traveled according to observers on the spacecraft? 15.18 light-years Previous Answers Submit Previous Answers Part D V = Correct What will the spacecraft occupants compute their speed to be from the results of part B and part C? 3.29 IVE ΑΣΦ Submit Previous Answers Request Answer ? X Incorrect; Try Again; 4 attempts remaining •C