Two small forces are exerted on a small 186kg asteroid by a pair of space tractors. F⃗ 1F⃗ 2==(−3.13N)î +(−4.72N)ĵ (10.58N)î +(−4.04N)ĵ What is the magnitude, in meters per squared second, of the acceleration of the asteroid?
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- An asteroid has a mass of m = 8.5 × 1012 kg and also has two rocket thrusters attached to it. One thruster supplies a force with x- and y- componentsF 1 = (8.0 × 107, 7.0 × 107) N while the other supplies a force with x- and y-components F 2 = (4.0 × 107, −2.0 × 107) N. (You may ignore the mass of the rocket thrusters and their fuel.) 1. What is the magnitude of the acceleration of the asteroid produced by the thrusters and in which direction does it act? 2. If the constant force acts in the same direction as the asteroids motion. calculate the time required to change the speed of the asteroid by 1.0ms-1 and therefore show that this is about 18 hours.At what distance above the surface of the earth is the acceleration due to the earth’s gravity 0.980 m/s20.980 m/s2 if the acceleration due to gravity at the surface has magnitude 9.80 m/s2?A 475-gram ball is traveling horizontally at 12.0 m/s to the left when it is suddenly struck horizontally by a bat, causing it to reverse direction and initially travel at 8.50 m/s to the right. If the bat produced an average force of 1275 N on the ball, for how long (in milliseconds) was it in contact with the ball? 5.64 6.64 7.64 8.64 9.64
- The highest spot on Earth is Mt. Everest, which is 8850 m above sea level. If the radius of the Earth (to sea level) is 6370 km, how much does the magnitude of g change between sea level and the top of Mt. Everest? (G = 6.67 × 10-11 N m2/kg2, and the mass of the Earth is 5.98 × 1024 kg.)Find the magnitude of the gravitational force (in N) between a planet with mass 6.00 ✕ 1024 kg and its moon, with mass 2.60 ✕ 1022 kg, if the average distance between their centers is 2.20 ✕ 108 m. N (b) What is the moon's acceleration (in m/s2) toward the planet? (Enter the magnitude.) m/s2 (c) What is the planet's acceleration (in m/s2) toward the moon? (Enter the magnitude.) m/s2A spaceship is midway between the earth and the moon when its engines fail. What is its acceleration? Assume that the distance from the center of the earth to the center of the moon is 3.8 x 108 m and the mass of the moon is 7.38 x 1022 kg.
- (a) Find the magnitude of the gravity force between a planet with mass 5.98 1024 kg and its moon, with mass 7.36 1022 kg, if the average distance between them is 3.84 108 m. (b) What is the acceleration of the moon toward the planet? (c) What is the acceleration of the planet toward the moon? (See Section 7.5.)The two objects in the figure are connected by a massless cable which passes over a massless and frictionless pulley, and mass m2 is on a horizontal frictionless surface. Assuming gravity acts downward in the figure, and the objects are moving with a common acceleration as m1 falls downward, what is the acceleration of the system? A) 2.45 m/s^2 B) 4.9 m/s^2 C) 7.35 m/s^2 D) 9.8 m/s^2A ball of mass 100 g, projected at an angle of 30° from the ground with an initial velocity of 11 m/s, Its horizontal and vertical components of its initial velocity are : _____ and ______. a. 5.5 m/s ; 9.5 m/s b. 9.5 m/s ; 5.5 m/s c. 9.5 m/s ; 1.5 m/s d. 9.8 m/s ; 5.5 m/s
- The force due to gravity on an object with mass $m$ at a height $h$ above the surface of the earth is\[F-\frac{m g R^{2}}{(R+h)^{2}}\]where $R$ is the radius of the earth and $g$ is the acceleration due to gravity.(a) Express $F$ as a series in powers of $h / R$.Ball #1 (mass m, velocity v) and ball #2 (mass 3 m, velocity 3 v) roll horizontally off a table of height h. The balls hit the floor at horizontal distances x1 and x2 from the base of the table, respectively. Which statement is true? a) x2 = x1 / 9 b) x2 = 9 x1 c) x2 = x1 / 3 d) x2 = 3 x1 e) x2 = x1At t = 0, a cart of mass m = 5 kg starts rolling down an incline, making an angle α = 20o with the horizontal. Initially the cart rolls down with no friction, but after traveling a distance of ∆ = 10 m it encounters a rough surface, where the coefficient of friction is k = 0.45. Find the acceleration of the cart along the incline (positive direction is downhill) after it encounters the rough surface. A.9.8 m/s2 B.9.2 m/s2 C.7.7 m/s2 D.3.6 m/s2 E.3.4 m/s2 F.-0.8 m/s2
