8.37. What initial velocity must be given to a 5-kg mass if it is to rise to a height of 10 m? What is the total energy at any point in its path?
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8.37. What initial velocity must be given to a 5-kg mass
if it is to rise to a height of 10 m? What is the total
energy at any point in its path?
Ans. 14 m/s, 490 J](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49862da8-80a0-434a-9e00-3d229f3c0e56%2F102cfa36-2903-4297-982c-623261204baf%2Fw4phn12_processed.jpeg&w=3840&q=75)
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- Consider the process of escaping from the solar system starting from the surface of Earth. Assume there are no other bodies involved. Earth has an orbital speed about the Sun of 29.8 km/s. Hint: 2GM does not apply. Use mv,? GM_m GM m 2 GM-m GMs" which includes the potential energy of both Earth and the Sun. 2.5 V. esc 2,E (a) What minimum speed relative to Earth (in km/s) would be needed? km/s In what direction should you leave Earth? O opposite the direction of Earth's orbital velocity O towards the Sun O away from the Sun O in the direction of Earth's orbital velocity (b) What will be the shape of the trajectory? O a circle O an ellipse O a hyperbola O a parabolaThe sun generates energy through nuclear fusion, which converts mass intoenergy. If the sun radiates 3.8 × 1026 W of power, calculate the rate at which the sun losesmass (i.e., kg/s).4. A lkg mass initially at rest is accelerated by a 30N force, continuously, for a full year. How fast is it going at the end of that year? (If your answer is larger than the speed of light, you've done something wrong!). Hint: F = Ap/At.
- H2. Suppose a particle of constant mass m with position x > 0, moves in one space dimension under the influence of the gravitational force of another point particle of constant mass M sitting at x = 0, i.e. the attracting force is F: (a) Using Newton's second law, show that d -mx². dt GmM x² i. GmM X = 0. dv dv (i.e., the total energy, sum of kinetic and potential energy, is conserved). (b) Using the change of variables var dr, solve the equation of motion and determine the = dx velocity of the particle v(x) as a function of x assuming it starts with zero velocity at xo. Does the particle's speed in x O depend on the initial position? dt' =How to find Kinetic Energy? KE= 1/2mv1 2 m= 60 grams v1= 688.75Redo Exercise 238 from Section 1.4, but instead of a weather satellite with a mass of 1400 kg, calculate how many Joules of work it would take to elevate an almond with a mass of 0.0012 kg to the same altitude. Enter your answer as just a number (no units), rounded to two significant digits (remember, that's not the same as two decimal places!)
- Let's consider two vectors, A = (-7, 10), B = (-5, -8), and C = (-1, 6) as shown below. A C B What is the magnitude of A+ B+ C? Answer What is the direction (8) of A+B+C relative to +x-axis? a-839 b. 20 C-85 3 d. 148°The escape velocity from a massive object is the speed needed to reach an infinite distance from it and have just slowed to a stop, that is, to have just enough kinetic energy to climb out of the gravitational potential well and have none left. You can find the escape velocity by equating the total kinetic and gravitational potential energy to zero E=12mv2esc−GmM/r=0E=12mvesc2−GmM/r=0 vesc=2GM/r−−−−−−√vesc=2GM/r where GG is Newton's constant of gravitation, MM is the mass of the object from which the escape is happening, and rr is its radius. This is physics you have seen in the first part of the course, and you should be able to use it to find an escape velocity from any planet or satellite. For the Earth, for example the escape velocity is about 11.2 km/s, and for the Moon it is 2.38 km/s. A very important point about escape velocity: it does not depend on what is escaping. A spaceship or a molecule must have this velocity or more away from the center of the planet to be free…Pls help ASAP.