of ways to play the classic game "spin the bottle". The figure below shows three ways. In each case, assume that the magnitude of the force is the same. B A amb B In which case will the magnitude of the torque be greatest? m C A B C it's not possible to tell without specifying the size of the grid spacing
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- A force F = (7i + 3j + 3k) N is applied to a point with position vector r = (6i + 3j + k) m. Find the torque due to this force about the axis passing through the origin. (Express your answer in vector form.) Torque= ______ N*MConsider an hydrogen-like atom with a very light particle of mass m rotating around a heavy particle of mass M which is much greater than m. The charge of the heavy particle is -e and the charge of the lighter particle is +3e. The light particle executes uniform circular motion about its center of rotation which is where the heavy particle is located. Assume that the centripetal acceleration of the lighter particle is due essentially only to the Coulomb force of attraction between the two particles. Given that the orbital angular momentum of the light particle around its center of rotation is L = mvr =ħ, where v is the lighter particle's speed and r is its distance from the center of rotation, determine the speed of the lighter particle relative to the heavy particle. ke² HINT: you might want to make use of the relation hc 1 Recall that: ħ = 1.06 x 10-34 J-s; k= 4π€0 137. = 9 x 10⁹ Nm²/C² and e = 1.6 × 10-19 C.The figure below shows an angler with a fishing rod that makes an angle of 20.0° above the horizontal. The distance from the angler's hand to the tip of the rod isL = 2.18 m. A fish is on the line, and it pulls the line with a force of F = 109 N at an angle 37.0° below the horizontal. What is the magnitude of the torque (in N· m) exerted by the fish about an axis perpendicular to the page and passing through the angler's hand? 20.0° 37.0° I 20.0° N. m
- A triangular plate is acted on by three forces, as in the figure. Taking the +z- direction to be out of the screen, calculate the net torque (magnitude and direction) about red point O if d₁ = 2.7 m, d₂ = 1.6 m, F₁ = 27 N, F₂ = 47 N, F3 = 52 N, 02 = 57°, and 03 = 45°. F3 03 27 = d₂ 102 k N.m F2 d₁ F₁In the figure, three forces of the same magnitude are applied to a particle at the origin (acts directly into the plane of the figure). Rank the forces according to the magnitudes of the torques they create about the point P2, greatest first. T1, T2 and T3 are the corresponding torques for forces 1, 2 and 3. Ps P2 F1 O T2 = T3 > T1 O T1 > T2 > T3 O T1 = T2 > T3 T2 T3 > T1 T3 > T2 > T1The figure below shows a fisherman with a fishing pole that makes an angle of 20.0° above the horizontal. The distance from the fisherman's hand to the tip of the pole is L = 1.87 m. A fish is on the line, and it pulls the line with a force of F = 124 N at an angle 37.0° below the horizontal. What is the magnitude of the torque (in N · m) exerted by the fish about an axis perpendicular to the page and passing through the fisherman's hand?
- . Archeologists in Egypt are attempting to open a 2.57-m-wide door in the tomb of Tutankhamen. Miles, one of the rookie archeologists, pushes perpendicularly on the door with a force of 894 N. How much torque does Miles exert on the door?In figure forces F1 and F2 have magnitudes 20N and 15N respectively and act on a disk nailed at point P as shown. a) What torque (magnitude and direction) does each of these forces exert on the disk about point P? b) What is the net torque exerted? y 60° m 45° X 6 mA square, 0.144 m on a side, is mounted so that it can rotate about an axis that passes through the center of the square. The axis is perpendicular to the plane of the square. A force of 10.5 N lies in this plane and is applied to the square. What is the magnitude of the maximum torque that such a force could produce? Number Units
- Discuss the motion of the bead according to the equation of motionq¨2 − ω2sin2α q = −g cos αas completely as you can. Find explicit solutions. What will happen if the beadis slightly displaced from the point where it has no acceleration.Text Predictions: On e to search w S 4. Rank the torques in order from largest to smallest: A: mass mo, radius ro B: mass 2mo, radius ro 2Fo Fo Accessibility: Investigate 5 X alt E D || C R F 1 T JL G 6 B H C: mass mo, radius 2ro 7 hp 8 U J N A Fo M D: mass 2mo, radius 2ro fio ( JO O K > O L 2Fo Focus AA CO 441 + = 4- { PUOL Р 46 alt 80°F insert ? 8:40 AM 6/14/202 prt sc backaceIn the overhead view of the figure, five forces of the same magnitude act on a strange merry-go-round; it is a square that can rotate about point P, at midlength along one of the edges. F1 F2 F₂ Rank the forces according to the magnitude of the torque they create about point P. If multiple forces rank equally, use the same rank for each, then exclude the intermediate ranking (i.e. if objects A, B, and C must be ranked, and A and B must both be ranked first, the ranking would be A:Greatest, B:Greatest, C:Third greatest). If all forces rank equally, rank each as 'Greatest F3 F4 75 F₁ ◆ +