CT6-0 (Vector review)The vector Ar is shown. What is Ax?A: Ax = A cosB: Ax = A sinC: Neither of these.Answer: neither of these. The x-component of A is negative. Ax = -A sinx y CT6-1. A mass m is pulled along a frictionless table by constant force external force Fextat some angle above the horizontal. The magnitudes of the forces on the free-body diagram have not been drawn carefully, but the directions of the forces are correct. Which statement below must be true?A: mg > N B: N > mg C: N=mgAnswer: mg>N. Since there is no acceleration in the y-direction, Fy0, the forces up (N + Fextsin) must cancel the forces down (mg). The y-component of the Fext force isassisting the table in holding up the mass, so the table does not have to exert as large a force as it would if there were no Fext.mg N F ext FextCT6-2. A mass m is accelerates downward along a frictionless inclined plane. The magnitudes of the forces on the free-body diagram have not been drawn carefully, but thedirections of the forces are correct. Which statement must be true?A: mg > N B: N > mg C: N=mgAnswer: mg > N. Since there is no acceleration along the (tilted) y-axis, the y-component of the mg-force must be equal in magnitude to N.mg N y x y-component of Fgrav mg N aCT6-2. A rider in a "barrel of fun" finds herself stuck with her back to the wall. Which diagram correctly shows the forces acting on her? A B C D EAnswer: A The person is moving in a circle, therefore she is accelerating toward the center of the circle. Therefore, there must be a net force acting on her toward the center of the circle. That force is the normal force of the wall pressing against her back. There is no outward "centrifugal force". Centrifugal forces are examples of "fictitious forces" or pseudo-forces. Such forces do not exist. (Sometimes pretending such forces exist makes problem solving mathematically easier. But in my opinion, they also cause terrible confusion.)Pink Blue Green Purple Yellowmg Ffri ction NCT5-11 A bucket containing a brick is swung in a circle at constant speed in a vertical plane as shown. The bucket is swung fast enough that the brick does not fall out.The net force on the brick as it is swung has maximum magnitude at position.A: Top.B:Bottom.C: RightD: The net force has the same magnitude at all positions.Consider the normal force exerted on the brick by the bucket when the bucket is at the three positions shown: R, T, B. The magnitude of the normal force is a minimum at position...A: Top. B: Bottom. C: RightD: The normal force has the same magnitude at all positions.Answers: The net force has the same magnitude at all positions. Since this is circular motion with constant speed, the magnitude of the acceleration (a = v2/R) is constant and so is Fnet = ma = mv2/R .The normal force is minimum at position T(top). At both positions B and T, the normal force N when vector-added to the weight mg is the net force Fnet. Since Fnet and mg are constant in magnitude, N is minimum when it points in the same direction as mg . NRBTR B T mg N mg mg N N
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