A rocket powered car is set inside a circular track and ignited. Pressure sensors on the wall of the track measure the centripetal acceleration of the car as a function of time to be ac (t) = (9 m/s®) tª + (42 m/s*) t² + (49 m/s³) If the radius of the track is 2.28 m, what is the tangential acceleration of the rocket car at t = 6.76 s? tangential acceleration: m/s?
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- To create artificial gravity, the space station shown in the drawing is rotating at a rate of 2.10 rpm. The radii of the cylindrically shaped chambers have the ratio rA/rB = 5.00. Each chamber A simulates an acceleration due to gravity of 8.80 m/s2. Find values for (a) rA, (b) rB, and (c) the acceleration due to gravity that is simulated in chamber B.On the International Space Station an object with mass m = 440 g is attached to a massless string of length L = 0.61 m. The string can handle a tension of T = 5.8 N before breaking. The object undergoes uniform circular motion, being spun around by the string horizontally.What is the maximum speed v the mass can have before the string breaks? Give your answer in units of m/s.A rocket, launched from the Earth, shuts off its engines when its speed is 5.10 km/s. It reaches a maximum altitude of 2600 km before it falls back to Earth. At what altitude did the rocket's engines shut off? The mass and radius of the Earth are 5.97 1024 kg and 6.37 106 m, respectively. M
- A rocket powered car is set inside a circular track and ignited. Pressure sensors on the wall of the track measure the centripetal acceleration of the car as a function of time to be ?c(?)=(4 m/s6)?4+(28 m/s4)?2+(49 m/s2) If the radius of the track is 3.28 m, what is the tangential acceleration of the rocket car at ?=5.51 s?A 1.80 kg toy race car is slowing down while travelling around a circular horizontal track. If the track has a diameter of 1.51 m and the coefficient of rolling friction between the track and the race car is 0.260, what is the magnitude of angular acceleration?An astronaut, whose mission is to go where no one has gone before, lands on a spherical planet in a distant galaxy. As she stands on the surface of the planet, she releases a small rock from rest and finds that it takes the rock 0.480 s to fall 1.90 m. If the radius of the planet is 8.60 * 107 m, what is the mass of the planet?
- A uniform, solid sphere, of radius R=0.84km, produces a gravitational acceleration of ag on its surface. At what distance from the sphere's center are there points (a) inside and (b) outside the sphere, where the gravitational acceleration is ag/3?In 2014, the Rosetta space probe reached the comet Churyumov– Gerasimenko. Although the comet’s core is actually far from spherical, in this problem we’ll model it as a sphere with a mass of 1.0 x 1013 kg and a radius of 1.6 km. If a rock were dropped from a height of 1.0 m above the comet’s surface, how long would it take to hit the surface?A block of mass m1 = 30.0 kg (starting from the rest) is going down an inclined plane at angle θ = 30° is connected by a massless cord that is wrapped around a uniform disk of mass M = 1.50 kg and radius R = 10.0 cm to a second block of mass m2 = 5.00 kg hanging vertically. The disk can rotate about a fixed horizontal axis through its center; the cord cannot slip on the disk. The coefficient of kinetic friction between m1 and the surface is μk = 0.150. Find (a) the magnitude of the acceleration for the blocks, (b) the tension T1 in the cord at the left and (c) the tension T2 in the cord at the right. After m1 moves 2 m, (d) What is the speed of m2? (e) How long will it take for m1 to travel 2.00 m? (f) What is the work done by the net force on m1? (h) What is the work done by the net force on m2? Section D, E, F, H
- A block of mass m1 = 30.0 kg (starting from the rest) is going down an inclined plane at angle θ = 30° is connected by a massless cord that is wrapped around a uniform disk of mass M = 1.50 kg and radius R = 10.0 cm to a second block of mass m2 = 5.00 kg hanging vertically. The disk can rotate about a fixed horizontal axis through its center; the cord cannot slip on the disk. The coefficient of kinetic friction between m1 and the surface is μk = 0.150. Find (a) the magnitude of the acceleration for the blocks, (b) the tension T1 in the cord at the left and (c) the tension T2 in the cord at the right. After m1 moves 2 m, (d) What is the speed of m2? (e) How long will it take for m1 to travel 2.00 m? (f) What is the work done by the net force on m1? (h) What is the work done by the net force on m2?One model for a certain planet has a core of radius R and mass M surrounded by an outer shell of inner radius R, outer radius 2R, and mass 4M. If M= 4.1 * 1024 kg and R = 6.0 *106 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet?Figure shows a conical pendulum, in which the ball with a mass of m=10.0 kg moves in a horizontal circle at constant speed. If the wire has a length of L=10.0 m and makes an angle of θ=30.0° with the vertical, determine (a) the horizontal (Tx) and vertical (Ty)components of the force exerted by the wire on the ball (b) the radial acceleration of the ball (c) the speed of the ball. cos30o =sin60o=0.866 cos60o =sin30o=0.500 g=9.8 m/s2