A luminous point is moving at speed vo toward a spherical mirror with radius of curvature r, along the central axis of the mirror. Assume the mirror is concave, with r = 25 cm, and let v0 = 5.4 cm/s. Find v1 (the speed of the image of the point) when (a) p = 37 cm (far outside the focal point), (b) p = 13 cm (just outside the focal point), and (c) p = 9.8 mm (very near the mirror). (a) Number Units (b) Number Units (c) Number Units
If y(x,t) = (5.9 mm) sin[kx + (830 rad/s)t + ϕ] describes a wave traveling along a string, how much time does any given point on the string take to move between displacements y = +3.5 mm and y = −3.5 mm? Number Units
A 25 kg body is moving through space in the positive direction of an x axis with a speed of 170 m/s when, due to an internal explosion, it breaks into three parts. One part, with a mass of 11 kg, moves away from the point of explosion with a speed of 98 m/s in the positive y direction. A second part, with a mass of 6.0 kg, moves in the negative x direction with a speed of 540 m/s. What are the (a) x-component and (b) y-component of the velocity of the third part? (c) How much energy is released in the explosion? Ignore effects due to the gravitational force. (a) Number Units (b) Number Units (c) Number Units
Two particles oscillate in simple harmonic motion along a common straight-line segment of length 0.60 m. Each particle has a period of 1.8 s, but they differ in phase by π/5 rad. (a) How far apart are they 0.59 s after the lagging particle leaves one end of the path? (b) Are they then moving in the same direction, toward each other, or away from each other? (a) Number Units (b)
A 22 kg body is moving through space in the positive direction of an x axis with a speed of 140 m/s when, due to an internal explosion, it breaks into three parts. One part, with a mass of 6.2 kg, moves away from the point of explosion with a speed of 170 m/s in the positive y direction. A second part, with a mass of 4.6 kg, moves in the negative x direction with a speed of 700 m/s. What are the (a) x- component and (b) y-component of the velocity of the third part? (c) How much energy is released in the explosion? Ignore effects due to the gravitational force. (a) Number Units (b) Number Units (c) Number Units
In the figure, a 0.400 kg ball is shot directly upward at initial speed 53.4 m/s. What is its angular momentum about P, 3.77 m horizontally from the launch point, when the ball is (a) at maximum height and (b) halfway back to the ground? What is the torque on the ball about P due to the gravitational force when the ball is (c) at maximum height and (d) halfway back to the ground? The sign convention is that a torque is positive if it would cause counterclockwise rotation.