A small ball with mass 0.50 kg moves in a vertical circle on the inside of a frictionless circular track with radius of curvature 0.80 m, as shown in the sketch. What minimum speed must the ball have at point A, at the top of its circular path, in order not to lose contact with track at that point?
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- A pendulum consists of a small object called a bob hanging from a light cord of fixed length, with the top end of the cord fixed, as represented in Figure OQ5.6. The bob moves without friction, swinging equally high on both sides. It moves from its turning point A through point B and reaches its maximum speed at point C. (a) Of these points, is there a point where the bob has nonzero radial acceleration and zero tangential acceleration? If so, which point? What is the direction of its total acceleration at this point? (b) Of these points, is there a point where the bob has nonzero tangential acceleration and zero radial acceleration? If so, which point? What is the direction of its total acceleration at this point? (c) Is there a point where the bob has no acceleration? If so, which point? (d) Is there a point where the bob has both nonzero tangential and radial acceleration? If so, which point? What is the direction of its total acceleration at this point? Figure OQ5.6A skier weighing 600 N goes over a frictionless circular hill of radius R 20 m ). Assume that the effects of air resistance on the skier are negligible. As she comes up the hill, her speed is 8.0 m/s at point B, at angle u= 20. (a) What is her speed at the hilltop (point A) if she coasts without using her poles? (b) What minimum speed can she have at B and still coast to the hilltop? (c) Do the answers to these two questions increase, decrease, or remain the same if the skier weighs 700 N instead of 600 N?A toy car with a mass of 0.150kg goes through the top of a loop the loop with a radius of 0.300m while experiencing a downward normal force with a magnitude of 7.35N. What is the speed of the toy car in meters per second as it goes through the top of the loop?
- A Purple Block about (mA = 24 kg) glides along a rail, it starts at point 1 with a height H1 = 5.40 m). (Entire rail is frictionless) and before entering a loop the (radius R = 1.80 m). Three more points 2, 3, and 4 are all marked on the sides as well as on the top of these loops. The purple block then comes out of the loop while travelling at a speed of 12 m/s. Has a t-bone collision with the blue block which is mB = 8 kg with a speed of 6 m/s before the collision happens. After the accident, purple block's speed is 5.30 m/s and is still moving in the same direction it was before the collision. (see picture) A)What kind of collision is this? For the purple block: (parts a-b)a.) speed of block have at point 1?v1 = _____ m/sb.) At point 2, speed of the block: v2 = _____ m/sthe force acting on the block not to closely to the circle:______ N, with the motion, against the motion, it is zero force acting on the block, radial to the circle:______ N, toward the center of the loop, away…A 2.8 kg block slides over the smooth, icy hill shown in Fig. . The top of the hill is horizontal and 70 m higher than its base. What minimum speed must the block have at the base of the 70 m hill to pass over the pit at the far (righthand) side of that hill?A bead is sliding frictionlessly in the orbit in the figure. If the bead is released from the height h = 4R, what will its velocity at point A be? (gravitational acceleration g)
- Can you please provide a complete solution set to this problem? A rollercoaster car is traveling on a track and approaching a loopped portion of track. What is the minimum speed needed at the bottom of the loop to clear the loop? The diameter is 15 meters.A roller-coaster travels over a vertical, circular loop of radius R = 27.8 m. If it travels without friction along the track, what is the minimum speed required at the bottom of the loop such that the roller-coaster remains in contact with the track at the top of the loop?A roller coaster goes around a vertical loop that has a diameter of 40 m. What is the minimum speed that the roller coaster car must go at the top of the loop to stay on track? (the total mass is 600 kg) (
- An uncrewed mission to the nearest star, Proxima Centauri, is launched from the Earth's surface as a projectile with an initial speed of 43.1 km/s, just enough for the spacecraft to escape the Earth's gravity and leave the solar system. Ignoring air resistance and the Earth's rotation, what is the speed of the spacecraft when it is more than halfway to the star? Assume we are ignoring the effect of the Sun on the spacecraft.A block of mass 2 kg begins with velocity 2.3 m/s at the top of a curved track at a height h= 9.9 m and travels around a circular loop of radius R. There is negligible friction between the block and the track between points A and D, but the coefficient of kinetic friction on the horizontal surface between points D and E is u=0.4. If the block stops at point E, what is the distance (in m) between points D and E? A 2R ВA car in an amusement park ride rolls without friction around a track. The car starts from rest at point A at a height h above the bottom of the loop. Treat the car as a particle. What is the minimum value of h (in terms of R) such that the car moves around the loop without falling off at the top (point B)? If the car starts at height h= 4.50 R and the radius is R1 = 17.0 m, compute the speed of the passengers when the car is at point C, which is at the end of a horizontal diameter. Compute the radial acceleration of the passengers when the car is at point C, which is at the end of a horizontal diameter.