**Problem Description:**Dima pulls directly backward with a force \( F = 111 \, \text{N} \) on the end of a \( 2.00 \, \text{m} \)-long oar. The oar pivots about its midpoint. At the instant shown, the oar is completely in the yz-plane and makes a \( \theta = 39.0^\circ \) angle with respect to the water's surface.**Objective:**Derive an expression for the torque vector \( \vec{\tau} \) about the axis through the oar's pivot. Express the torque using \( ijk \) vector notation.**Equation Format:**\[\vec{\tau} = \tau_x \, \mathbf{i} + \tau_y \, \mathbf{j} + \tau_z \, \mathbf{k}\]\(\vec{\tau} =\) \(\boxed{\phantom{}} \, \text{N}\cdot\text{m}\)---**Diagram Explanation:**1. **Side View:** - Shows the oar positioned in the yz-plane. - The angle \( \theta = 39.0^\circ \) is formed between the oar and the horizontal plane (water's surface). - Axes are indicated with \( z \) pointing upwards and \( y \) running horizontally parallel to the surface.2. **Aerial View:** - Displays the oar from a top-down perspective. - The force \( F = 111 \, \text{N} \) is applied downward along the oar. - The axes \( x \) and \( y \) are marked, with \( y \) being the lengthwise direction of the oar.Given these views, use the torque formula \( \vec{\tau} = \vec{r} \times \vec{F} \) to calculate the torque vector components \( \tau_x, \tau_y, \) and \( \tau_z \).

Answered: Image /qna-images/answer/6ef4dade-eba4-4fc0-9e1a-e163be667b35.jpg

Macmillan Learnin Dima pulls directly backward with a force F = 111 N on the end of a 2.00 m-long oar. The oar pivots about its midpoint. At the instant shown, the oar is completely in the yz-plane and makes a 0 = 39.0° angle with respect to the water's surface. Derive an expression for the torque vector 7 about the axis through the oar's pivot. Express the torque using ijk vector notation. 7 = Txi+ Ty j + T₂ k 7 = N.m Side view Aerial view 0 F

Macmillan Learnin Dima pulls directly backward with a force F = 111 N on the end of a 2.00 m-long oar. The oar pivots about its midpoint. At the instant shown, the oar is completely in the yz-plane and makes a 0 = 39.0° angle with respect to the water's surface. Derive an expression for the torque vector 7 about the axis through the oar's pivot. Express the torque using ijk vector notation. 7 = Txi+ Ty j + T₂ k 7 = N.m Side view Aerial view 0 F

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

(a) A person opens a 1.20 m wide door by pushing on it with a force of 57.5 N applied at the center of the door, at an angle perpendicular to the door's surface. What magnitude of torque (in N · m) is applied about an axis through the hinges? _________N · m (b) A man opens the same door, using the same force, again directed perpendicular to the surface, but now the force is applied at the edge of the door. What magnitude of torque (in N · m) is applied about the axis through the hinges now? _________N · m
A hinged beam, 92.5 kg, is supported by a horizontal cable as in the figure. The length of the cable is 2.00 m and the length of the beam is 3.00 m. Find: (a) the torque produced by gravity on the beam, (b) the tension in the cable, (c) the horizontal and vertical components of the force from the hinge, and (d) the magnitude and direction of the force from the hinge.
For two existing torques, what third force at a given distance from the pivot will balance them? Imagine a meter stick set up as in the figure. It hangs from a central bracket, and two hanging masses can hang from it from each of their brackets. At a third location, a force probe can either pull up or pull down on the stick, depending on what is needed to balance the stick. The mass of the meter stick is 120 g. sketch the situation (drawing r1, r2, r3, F1, F2, and F3) and determine the magnitude (value) and direction (+ or -) of each torque. Don't include the mass of a bracket that would hold the hanging mass in place; assume the mass listed is the entire mass hanging at that point. For each trial, use the principle of equilibrium (where the sum of torques is zero) to calculate the third, unknown force acting at x3
(a) A woman opens a 1.35 m wide door by pushing on it with a force of 44.5 N applied at the center of the door, at an angle perpendicular to the door's surface. What magnitude of torque (in N · m) is applied about an axis through the hinges? (b) A girl opens the same door, using the same force, again directed perpendicular to the surface, but now the force is applied at the edge of the door. What magnitude of torque (in N · m) is applied about the axis through the hinges now?
Find τF the torque about point P due to the force applied by the Achilles' tendon. Express your answer in terms of F, ϕ, and x.
The drawing below shows two forces acting on a rigid beam. The blue dot is the center of mass of the beam. The forces (red arrows) are equal in magnitude. Consider the net force on the beam and net torque about its center. Which of the following statements are true? Check ALL that apply. The net force is zero. The net force is not zero. The net torque is zero. O The net torque is not zero.
A solid sphere, made of acrylic plastic with a density of 1.1 g/cm3,1.1 g/cm3, has a radius of 5.0 cm.5.0 cm. A very small "eyelet" is screwed into the surface of the sphere and a horizontal support rod is passed through the eyelet, allowing the sphere to pivot around this fixed axis, as shown in the figure. If the sphere is displaced slightly from equilibrium on the surface of Earth, determine the period ?T of its harmonic motion when it is released.
While on a camping trip, a man would like to carry water from the lake to his campsite. He fills two, non-identical buckets with water and attaches them to a 1.51 m long rod. Since the buckets are not identical, he finds that the rod balances about a point located at a length I 0.0367 m from its midpoint, as shown. The weight of the rod and empty buckets is negligible compared to the weight of the water, and the buckets are not shown to scale. Which bucket holds more water? bucket 2 1 bucket 1 They hold the same amount of water. How much more water does the heavier bucket contain, expressed as a percentage? percentage:
For two existing torques, what third force at a given distance from the pivot will balance them? Imagine a meter stick set up as in the figure. It hangs from a central bracket, and two hanging masses can hang from it from each of their brackets. At a third location, a force probe can either pull up or pull down on the stick, depending on what is needed to balance the stick. The mass of the meter stick is 120 g. sketch the situation (drawing r1, r2, r3, F1, F2, and F3) and determine the magnitude (value) and direction (+ or -) of each torque. Don't include the mass of a bracket that would hold the hanging mass in place; assume the mass listed is the entire mass hanging at that point. For each trial, use the principle of equilibrium (where the sum of torques is zero) to calculate the third, unknown force acting at x3
A uniform 8.00 m, 1500 kg beam is hinged to a wall and supported by a thin cable attached 2.00 m from the free end of the beam, as shown in the figure. The beam is fixed to the wall by a hinge at an angle of 30.0 above the horizontal. The angle between the cable and the beam is 40.0. MO 400 What is the direction of the torque exerted by the beam around the point where the cable is attached to the beam? O clockwise O counterclockwise
The center of mass of the arm shown in the figure is at point A. Find the magnitudes (in N) of the tension force F and the force F which hold the arm in equilibrium. (Let 8 = 24.0°.) Assume the weight of the arm is 48.3 N. IF 8.00 cm 29.0 cm 1₂ 354 X Draw a diagram showing the forces and distances. Find the sum of the torques about point O, and set this equal to zero. Solve your equation for F₁. N 340.30 X Apply Newton's second law in the x and y directions, and solve for F Sx Pythagorean theorem to calculate F. . N and F You will need your value of F. Then use the sy'