An asteroid of mass m = 8.5 × 10¹² kg has two rocket thrusters attached to it. One thruster supplies a force with r- and y- components F₁ = (8.0 × 107, 7.0 × 107) N while the other supplies a force with r- and y-components F2 = (4.0 × 107, -2.0 × 107) N. (You may ignore the mass of the rocket thrusters and their fuel.) (i) Preparation: Draw a sketch showing the two forces acting on the asteroid. Your sketch should be drawn (approximately) to scale. Use your sketch to estimate (without calculation) the resultant force on the asteroid. Include the resultant force on your sketch. (ii) Working: What is the magnitude of the resultant force and in which direction does it act? (iii) Checking: Compare your calculations from (a)(ii) with your sketch from (a)(i). Do your results agree? At what distance from the Earth, in kilometres, would the force calculated in (a) have the same magnitude as that due to the gravitational attraction between the asteroid and the Earth? (i) What is the magnitude of the acceleration of the asteroid produced by the thrusters and in which direction does it act? (ii) If the constant force calculated in (a) acts in the same direction as the asteroid's motion, calculate the time required to change the speed of the asteroid by 1.0 ms-¹ and therefore show that this is about 18 hours.
An asteroid of mass m = 8.5 × 10¹² kg has two rocket thrusters attached to it. One thruster supplies a force with r- and y- components F₁ = (8.0 × 107, 7.0 × 107) N while the other supplies a force with r- and y-components F2 = (4.0 × 107, -2.0 × 107) N. (You may ignore the mass of the rocket thrusters and their fuel.) (i) Preparation: Draw a sketch showing the two forces acting on the asteroid. Your sketch should be drawn (approximately) to scale. Use your sketch to estimate (without calculation) the resultant force on the asteroid. Include the resultant force on your sketch. (ii) Working: What is the magnitude of the resultant force and in which direction does it act? (iii) Checking: Compare your calculations from (a)(ii) with your sketch from (a)(i). Do your results agree? At what distance from the Earth, in kilometres, would the force calculated in (a) have the same magnitude as that due to the gravitational attraction between the asteroid and the Earth? (i) What is the magnitude of the acceleration of the asteroid produced by the thrusters and in which direction does it act? (ii) If the constant force calculated in (a) acts in the same direction as the asteroid's motion, calculate the time required to change the speed of the asteroid by 1.0 ms-¹ and therefore show that this is about 18 hours.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:An asteroid of mass m = 8.5 × 10¹² kg has two rocket thrusters attached to
it. One thruster supplies a force with r- and y- components
F₁ = (8.0 × 107, 7.0 × 107) N while the other supplies a force with r- and
y-components F2 = (4.0 × 107, -2.0 × 107) N. (You may ignore the mass of
the rocket thrusters and their fuel.)
Transcribed Image Text:(i) Preparation: Draw a sketch showing the two forces acting on the
asteroid. Your sketch should be drawn (approximately) to scale.
Use your sketch to estimate (without calculation) the resultant
force on the asteroid. Include the resultant force on your sketch.
(ii) Working: What is the magnitude of the resultant force and in
which direction does it act?
(iii) Checking: Compare your calculations from (a)(ii) with your
sketch from (a)(i). Do your results agree?
At what distance from the Earth, in kilometres, would the force
calculated in (a) have the same magnitude as that due to the
gravitational attraction between the asteroid and the Earth?
(i) What is the magnitude of the acceleration of the asteroid
produced by the thrusters and in which direction does it act?
(ii) If the constant force calculated in (a) acts in the same direction as
the asteroid's motion, calculate the time required to change the
speed of the asteroid by 1.0 ms-¹ and therefore show that this is
about 18 hours.
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