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A satellite will travel indefinitely in a circular orbit around the earth if the normal component of its acceleration is equal to
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Vector Mechanics For Engineers
- At a certain point in the reentry of the space shuttle into the earth's atmosphere, the total acceleration of the shuttle may be represented by two components. One component is the gravitational acceleration g = 9.67 m/s² at this altitude. The second component equals 10.66 m/s² due to atmospheric resistance and is directed opposite to the velocity. The shuttle is at an altitude of 49.6 km and has reduced its orbital velocity of 28300 km/h to 16160 km/h in the direction = 1.23°. For this instant, calculate the radius of curvature of the path and the rate i at which the speed is changing. Answers: p= i = i i km m/s²arrow_forwardAt a certain point in the reentry of the space shuttle into the earth's atmosphere, the total acceleration of the shuttle may be represented by two components. One component is the gravitational acceleration g = 9.56 m/s2 at this altitude. The second component equals 11.25 m/s² due to atmospheric resistance and is directed opposite to the velocity. The shuttle is at an altitude of 47.9 km and has reduced its orbital velocity of 28300 km/h to 14750 km/h in the direction = 1.88°. For this instant, calculate the radius of curvature of the path and the rate i at which the speed is changing. Answers: p= i = i FU km m/s²arrow_forwardA satellite is in a circular orbit around Mars. It has a constant altitude and constant speed. The acceleration of the satellite is: tangential - direction opposite to the velocity radial - directed towards Mars O radial - directed away from Mars tangential - along the velocity zeroarrow_forward
- A 10 lb particle has forces of F= (3i+ 5j) lb and F,= (-7i+ 9j) lb acting on it. Determine the acceleration of the particle. A) (-0.4 i+ 1.4 j) ft/s² B) (-4 i+ 14 j) ft/s² C) (-12.9 i+ 45 j) ft/s² D) (13 i+ 4 j) ft/s²arrow_forwardThe radius of the earth around the sun (assumed to be circular) is 1.5x108 km, and the earth travels around this orbit in 365 days. Calculate th eradial acceleration of the earth toward the sun in m/s2. A 1.90 x 10-3 m/s² B 5.95 x 10-6 m/s2 C 5.95 x 10-3 m/s2 1.90 x 10-6 m/s2arrow_forwardThe robotic arm shown in figure below is programmed to move 0.5 kg sphere A in a vertical plane. The path of sphere A can be defined using the functions r = 0.5t − 0.5 cos(2πt) m and θ = 0.5 −0.2 sin(2πt) rad. At t = 2 s, determine a) Radial and transverse components of the force exerted on A by the robot’ jawsarrow_forward
- A girl operates a radio-controlled model car in a vacant parking lot. The girl’s position is at the origin of the xy coordinate axes, and the surface of the parking lot lies in the x-y plane. She drives the car in a straight line so that the x coordinate is defined by the relation x(t) = 0.5t3 - 3t2 + 3t2 + 3t + 2, where x and t are expressed in meters and seconds, respectively. Determine (a) when the velocity is zero, (b) the position and total distance travelled when the acceleration is zero.arrow_forwardA 100-kg box is towed to move horizontally from rest by a constant force P=200 N. The kinetic friction is μk =0.1. The angle of the force P is θ=30° with respect to the horizontal direction. The acceleration due to gravity is g=9.81 m/s2. (7) Calculate the the velocity at 2 seconds v= ___(m/s ) (two decimal places).arrow_forward2- The rotation of rod OA about O is defined by the relation 0 = n(4t² – 8t), where 0 and t are expressed in radians and seconds, respectively. Collar B slides along the rod so that its distance from 0 is r = 10 + 6 sin at, where r and t are expressed in inches and seconds, respectively. When t = 1 s, determine (a) the velocity of the collar, (b) the total acceleration of the collar, (c) the acceleration of the collar relative to the rod.arrow_forward
- A cyclist and her bike, with a mass of 70 kg, descend down the slope 01 4° at a certain constant speed without braking or pedaling. The slope changes sharply to an incline slope 02 = 3° at point A. If the cyclist does not perform any action but continues by inertia, determinate the magnitude of the acceleration of the bike just after passing through point A. Express the response in m/s2. 0₁ v = constant A 02arrow_forwardO 4. Moves downward at constant speed. QUESTION 20 A box of mass 400 kg is supported on a spring scale on the floor of a goods lift. The mass of the lift is 1900 kg. The lift is travelling from the 20th floor to the ground floor. At an instant when the deceleration of the lift is 1.2 ms 2 as it approaches the ground floor, what is the reading recorded by the scale? O 1.351 kg O 2.387 kg O 3.449 kg O 4.461 kg Click Save and Submit to save and submit. Click Save All Answers to save all answers.arrow_forwardThe motion of a particle is defined by the function x = at3 - bt2 - ct + d where x is in centimeters and t is in seconds When is the particle at rest if a = 1.3, b = 3.5, c = 8.3, and d = 5.2?arrow_forward
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