Phys Extra Practice Equilibrium

**Give Exact Trig Functions** sin 30° = 1/2 cos 30° = √3/2 tan 30° = 1/√3 sin 60° = √3/2 cos 60° = 1/2 tan 60° = √3 **Trig Identity:** sin²θ + cos²θ = 1 **PRACTICE QUESTIONS - EQUILIBRIUM** **Use the following information to answer the next question.** Four different forces are applied at different angles to the end of a   1 m long wooden beam, as shown in the given table. | Force (N) | Angle | |---|---| | 10 | 60° | | 15 | 45° | | 20 | 90° | | 30 | 30° | The other end of the beam is attached to a wall by a hinge, as shown in the figure. 1. Which of the forces will produce the greatest   torque about the hinge? * A. 10 N * B. 15 N * C. 20 N * D. 30 N **Use the following information to answer the next question.** A horizontal force of 15 N is applied to the bob of a 25 cm long pendulum. The mass of the bob is 3.0 kg. 2. The height that the bob will reach above its equilibrium position will be: * A. 2.7 cm * B. 4.1 cm * C. 11 cm * D. 22 cm **Use the following information to answer the next question.** A woodcutter wants to lift a wooden log that weighs 600 N with the help of a 5.0 m long board. The board is pivoted at a distance of 2.0 m from the log as shown in the given figure. Assume that the forces are vertical with respect to the board. 3. The magnitude of the minimum force (F) necessary to lift the log is: * A.   1.0 × 10² N * B. 4.0 × 10² N * C. 6.0 × 10² N * D. 9.0 × 10² N **Not for Reproduction** Use the following information to answer the next question. A platform is suspended by a supporting rope, as shown in the given figure. The tension in the   rope must not exceed 7.00 x 10^3 N or it will snap. The mass and length of the platform are 100 kg and 10.0 m, respectively. The support rope makes an angle of 60.0° with the platform. Assume that the load's center of mass resides on the very tip of the platform. 4. The maximum load on the platform that the rope can withstand is: A. 3.12   x 10^3 N B. 4.26 x 10^3 N C. 5.57 x 10^3 N D. 6.90 x 10^3 N 5. In order to lift the load, the minimum distance the worker would have to move the support is: A. 1 m away from the load B. 2 m away from the load C. 3 m toward the load D. 4 m toward the load 6. A body is in rotational equilibrium if the: A. net force acting on the body is zero B. net torque acting on the body is zero   C. sum of all the forces acting on the body is positive D. sum of all the torque acting on the body is positive 7. A car moving with uniform velocity on a horizontal road is in translational equilibrium because: A. no forces are   acting on it B. no air pressure is acting on it C. the sum of all external forces acting on it is zero D. the   friction between the tires and the road is balanced by Earth's gravity Segment of a Circle A segment of a circle is a region bounded by an arc and its chord. Area of a Segment Area of segment = Area of sector - Area of triangle   Example #4: Find the area of segment ZNAM to the nearest hundredth. circle with a 120degree sector and a triangle inscribed A = π(9)²(120°/360°) - 1/2(b)(h) A = π(81)(1/3) - 1/2(4.5)(9√3) A = 27π - 20.25√3 A ≈ 84.82 - 35.07 A ≈ 49.75 cm² Arc Length TERM DIAGRAM LENGTH Arc length circle with an arc labeled L = 2πr(θ/360°) Arc length is the distance along an arc measured in linear units. Example #5: Find the length FG. Give answers in terms of π and rounded to the nearest hundredth. circle with an arc FG and radius 8 cm L = 2π(8)(134°/360°) L = 16π(134/360) L = 16π(3/8) L = 6π ≈ 18.84 cm Example #6: Find the degree measure of an arc whose length is 3π and which is part of a circle of radius 12. 3π = 2π(12)(m/360°) 3 = 2(12)(m/360°) m = 45°