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Use the absolute derivative DA?/Du=dA?/du??(from ?? to ?)A? dx^?/du to prove that the inner (scalar) product of two vectors is preserved under parallel transport on a path if the connection defined on the manifold is a metric connection.
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Qustion: A pendulum is made by tying a 590 g ball to a 45 cm-long string. The pendulum is pulled 22o to one side, then released. Part A: What is the ball's speed at the lowest point of its trajectory? Part B: To what ang ...
Question: A rock climber stands on top of a 60 m high cliff hanger a pool of water. He throws two stones vertically downward 1.0 s apart and observes that they cause a single splash. The initial speed of the first stone ...
Can you help me with these questions? How can you tell if a single measurement is more precise than another? If the smallest division on a scale is 0.1 mL, to what precision should you take a volume measurement using tha ...
Question: A particle moving on the x-axis experiences a force given by Fx = qx 2 , where q is a constant. How much work is done on the particle as it moves from x=0 to x=d? Express your answer in terms of some or all of ...
Question: A series RLC circuit of R = 200 ohm, L = 0.900 H and C = 2.00 uF carries an rms current of 0.250 A with a frequency of 100 Hz. (a) What is the average rate at which electrical energy isconverted to heat in the ...
Question: A proton accelerates from rest in a uniform electric field of 610 N/C. At some later time, its speed is 1.4 106 m/s. (a) Find the magnitude of the acceleration of the proton. m/s2 (b) How long does it take the ...
Initially (at time t = 0) a particle is moving vertically at 5 m/s and horizontally at 0 m/s. Its horizontal acceleration is 1.6 m/s2. At what time will the particle be traveling at 57? with respect to the horizontal? Th ...
A projectile is fired at ground level with an initial speed of 36 m/s, at an angle of 34 degrees above the horizontal. It hits a target above the ground 2.4 seconds later. What is the horizontal distance in meters, from ...
Question: The potential difference between the surface of a 3.5 cmdiameter power line and a point 1.0 m distant is 3.6 kV. What is the line charge density on the power line? The response must be typed, single spaced, mus ...
Question: A plastic rod that has been charged to -15 nC touches a metalsphere. Afterward, the rod's charge is -10 nC. a. What kind of charged particle was transferred between the rodand the sphere, and in which direction ...
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