Physics 1301A/B Lecture Notes - Lecture 3: Parabolic Trajectory, Projectile Motion, Circular Motion

77 views5 pages

carolinesnotes

18 Jun 2017

School

Department

Course

Professor

For unlimited access to Class Notes, a Class+ subscription is required.

Document Summary

Chapter #3: motion in two and three dimensions. Vectors: a vector is a quantity that has both magnitude and direction. In two dimensions it takes two numbers to specify a vector. A vector can be represented by an arrow whose length corresponds to the vector"s magnitude: position is a vector quantity. An object"s position is speci ed by giving its distance from an origin and its direction relative to each axis. Here, r1 describes a point 2. 0m from the origin at a 30 angle to the axis. Adding vectors: to add vectors graphically, place the tail of the second vector at the head of the rst vector. Their sum is then the vector from the tail of the rst vector to the head of the second vector. Here, r2 is the sum of r1 and r. Vector arithmetic: to multiply a vector by a scalar, multiply the vector"s magnitude by the scalar. For a positive scalar the direction is unchanged.

Related Questions

A rectangular loop of wire has dimensions of 0.500 m by 0.300 m. The loop is pivoted at the x-axis and lies in the XY plane as shown in Figure P28.34. A uniform magnetic field of magnitude 1.50 T is directed at an angle of 40.0° with respect to the y axis with field lines parallel to the yz plane. The loop carries a current of 0.900 A in the direction shown. (Ignore gravitation.) We wish to evaluate the torque on the current loop.

(a) What is the direction of the magnetic force exerted on wire segment ab?

(b) What is the direction of the torque associated with this force about an axis through the origin?

(d) What is the direction of the torque associated with this force about an axis through the origin?

(e) Can the forces examined in parts (a) and (c) combine to cause the Loop to rotate around the x-axis?

(f) Can they affect the motion of the loop in any way? Explain.

(g) What is the direction of the magnetic force exerted on segment bc?

(h) What is the direction of the torque associated with this force about an axis through the origin?

(i) What is the torque on segment ad about an axis through magnetic force exerted on segment bc? (h) What is the direction of the torque associated with this force about an axis through the origin? (i) What is the torque on segment ad about an axis through the origin? O) From the point of view of Figure P28.34, once the loop is released from rest at the position shown, will it rotate clockwise or counterclockwise around the x-axis? (k) Compute the magnitude of the magnetic moment of the loop. (1) What is the angle between the magnetic moment vector and the magnetic field? (m) Compute the torque on the loop using the results to parts (k) and (1).

scarletbeetle53

This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page - find all choices before answering. Two vectors A and B lie in the xy plane and are given by A = Ax i + Ay j B = Bx i + By j, where Ax = 3.58 m, Ay = 2.85 m, Bx = 7.09 m, By = -6.36 m. Find the magnitude of R = A + B. Answer in units of m Find the angle theta (between -180 degree and + 180 degree with counterclockwise positive) that the vector R makes from the positive x axis. Answer in units of degree When the Sun is directly overhead, a hawk dives toward the ground at a speed of 7.23 m/s. If the direction of his motion is at an angle of 39.8 below the horizontal, calculate the speed of his shadow along the ground. Answer in units of m/s Vector A has a magnitude of 10 and points in the positive x-direction, Vector B has a magnitude of 17 and makes an angle of 32 degree with the positive x-axis. What is the magnitude of A - B? An airplane starting from airport A (lies 342 km east, then 531 km at 62.2 degree west of north, and then 778 km north to arrive finally at airport B. The next day, another plane flies directly from A to B in a straight line. In what direction should the pilot trawl in this direct flight? Use counterclockwise its the positive angular direction from due east, between the limits of - 180 degree ami 180 degree . Assume there is no wind during these flights. Answer in units of degree How far will the pilot travel in this direct flight? Answer in units of km A projectile is fired straight upward at 126 m/s. How fast is it moving at the instant it reaches the top of its trajectory? Answer in units of m/s How fast is it moving at the instant it reaches the top of its trajectory if the projectile is fired upward at 12 degree from the horizontal? Answer in units of m/s At one instant the velocity of a particle is and a very short time later its velocity has changed to . Qualitatively, what was the direction of the particle's acceleration during the interval between the first and second instance?

Consider an electric dipole whose dipole moment (a vector pointing from the negative charge to the positive charge) is oriented at an angle with respect to the y-axis. There is an external electric field of magnitude E (independent of the field produced by the dipole) pointing in the positive y-direction. The positive and negative ends of the dipole have charges +q and -q, respectively, and the two charges are a distance d apart. The dipole has a moment of inertia I about its center of mass. It will help you to imagine that the dipole is free to rotate about a pivot through its center.

A) What is the net force that the dipole experiences due to the electric field?

B) What is , the magnitude of the torque that the electric field exerts about the center of mass of the dipole?

C) Using the above result, find the potential energy associated with the dipole's orientation in the field as a function of the angle shown in the figure. Take the zero of the potential to occur when the dipole is at angle ; that is , .