Homework 8, torque 23-24-problems

peacock (ip6239) – Homework 8, torque 23-24 – tejeda – (KayaAPHY1 1) 1 This print-out should have 25 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. You will have approximately two weeks to complete this homework assignment. Collab- oration on homework is encouraged. How- ever, you must submit your own responses, and you may be required to show your in- dependent work to your HS Instructor. You are expected to access Quest daily to progress through this homework assignment. 001(part1of2)10.0points The arm of a crane at a construction site is 17.0 m long, and it makes an angle of 14 . 6 ◦ with the horizontal. Assume that the max- imum load the crane can handle is limited by the amount of torque the load produces around the base of the arm. What maximum torque can the crane with- stand if the maximum load the crane can handle is 751 N? Answer in units of N · m. 002(part2of2)10.0points What is the maximum load for this crane at an angle of 39 . 8 ◦ with the horizontal? Answer in units of N. 003 10.0points If the torque required to loosen a nut that is holding a flat tire in place on a car has a magnitude of 49 N · m, what minimum force must be exerted by the mechanic at the end of a 24 cm-long wrench to loosen the nut? Answer in units of N. 004(part1of2)10.0points The figure shows a claw hammer as it pulls a nail out of a horizontal board. Single point of contact 6 . 8 cm 29 ◦ F 28 cm If a force of magnitude 194 N is exerted horizontally as shown, find the force exerted by the hammer claws on the nail. (Assume that the force the hammer exerts on the nail is parallel to the nail). Answer in units of N. 005(part2of2)10.0points Find the force exerted by the surface on the point of contact with the hammer head. As- sume that the force the hammer exerts on the nail is parallel to the nail. Answer in units of N. 006(part1of2)10.0points A ladder rests against a vertical wall. There is no friction between the wall and the ladder. The coefficient of static friction between the ladder and the ground is µ = 0 . 613 .

peacock (ip6239) – Homework 8, torque 23-24 – tejeda – (KayaAPHY1 1) 2 W ℓ f θ h b F w N µ = 0 . 613 Consider the following expressions: A1: f = F w A2: f = F w sin θ B1: N = W 2 B2: N = W C1: ℓ F w sin θ = 2 F w cos θ C2: ℓ F w sin θ = ℓ W cos θ C3: ℓ F w sin θ = 1 2 ℓ W cos θ , where f : force of friction between the ladder and the ground, F w : normal force on the ladder due to the wall, θ : angle between the ladder and the ground, N : normal force on the ladder due to the ground, W : weight of the ladder, and ℓ : length of the ladder. Identify the set of equations which is cor- rect. 1. A2, B1, C2 2. A2, B1, C3 3. A1, B1, C1 4. A2, B1, C1 5. A2, B2, C1 6. A1, B1, C2 7. A1, B2, C2 8. A1, B2, C3 9. A1, B2, C1 10. A1, B1, C3 007(part2of2)10.0points Determine the smallest angle θ for which the ladder remains stationary. Answer in units of ◦ . 008 10.0points A 20 . 6 kg person climbs up a uniform ladder with negligible mass. The upper end of the ladder rests on a frictionless wall. The bottom of the ladder rests on a floor with a rough surface where the coefficient of static friction is 0 . 13 . The angle between the horizontal and the ladder is θ . The person wants to climb up the ladder a distance of 0 . 73 m along the ladder from the ladder’s foot. 20 . 6 kg 0 . 73 m 3 m θ µ = 0 . 13 µ = 0 What is the minimum angle θ min (between the horizontal and the ladder) so that the person can reach a distance of 0 . 73 m without having the ladder slip? The acceleration of gravity is 9 . 8 m / s 2 . Answer in units of ◦ . 009(part1of2)10.0points A square plate is produced by welding to-

peacock (ip6239) – Homework 8, torque 23-24 – tejeda – (KayaAPHY1 1) 4 What is the ratio between the rotational kinetic energy about the center of the sphere and the sphere’s total kinetic energy? 1. None of these 2. 3 5 3. 5 3 4. 7 2 5. 2 7 6. 2 5 7. 3 7 016 10.0points A regulation basketball has a 36 cm diameter and may be approximated as a thin spherical shell. How long will it take a basketball starting from rest to roll without slipping 1.9 m down an incline that makes an angle of 19 . 9 ◦ with the horizontal? The acceleration of gravity is 9 . 81 m / s 2 . Answer in units of s. 017 10.0points Two pans of a balance are 51 . 1 cm apart. The fulcrum of the balance has been shifted 0 . 403 cm away from the center by a dishonest shopkeeper. By what percentage is the true weight of the goods being marked up by the shopkeeper? Assume the balance has negligible mass. Answer in units of %. 018 10.0points The center of mass of a pitched baseball of radius 4 . 9 cm moves at 38 . 4 m / s. The ball spins about an axis through its center of mass with an angular speed of 198 rad / s. Treat the baseball as if it is a solid sphere rotating about its center ( I = 2 5 MR 2 ). Calculate the ratio of the rotational energy to the translational kinetic energy. 019(part1of2)10.0points A figure skater on ice spins on one foot. She pulls in her arms and her rotational speed increases. Choose the best statement below: 1. Her angular speed increases because air friction is reduced as her arms come in. 2. Her angular speed increases because by pulling in her arms she creates a net torque in the direction of rotation. 3. Her angular speed increases because her angular momentum is the same but her mo- ment of inertia decreases. 4. Her angular speed increases because her potential energy increases as her arms come in. 5. Her angular speed increases because her angular momentum increases. 6. Her angular speed increases due to a net torque exerted by her surroundings. 020(part2of2)10.0points And again, choose the best statement below: 1. When she pulls in her arms, her rotational kinetic energy must decrease because of the decrease in her moment of inertia. 2. When she pulls in her arms, her rotational kinetic energy is conserved and therefore stays the same. 3. When she pulls in her arms, her rota- tional potential energy increases as her arms approach the center. 4. When she pulls in her arms, the work she performs on them turns into increased rotational kinetic energy. 5. When she pulls in her arms, her moment

peacock (ip6239) – Homework 8, torque 23-24 – tejeda – (KayaAPHY1 1) 5 of inertia is conserved. 6. When she pulls in her arms, her angu- lar momentum decreases so as to conserve energy. 021(part1of2)10.0points A student sits on a rotating stool holding two 1 kg objects. When his arms are extended horizontally, the objects are 0 . 8 m from the axis of rotation, and he rotates with angular speed of 0 . 69 rad / sec. The moment of inertia of the student plus the stool is 6 kg m 2 and is assumed to be constant. The student then pulls the objects horizontally to a radius 0 . 4 m from the rotation axis. ϖ i ϖ f (a) (b) Calculate the final angular speed of the student. Answer in units of rad / s. 022(part2of2)10.0points Calculate the change in kinetic energy of the system. Answer in units of J. 023(part1of2)10.0points A merry-go-round rotates at the rate of 0 . 19 rev / s with an 92 kg man standing at a point 2 . 3 m from the axis of rotation. What is the new angular speed when the man walks to a point 0 m from the center? Consider the merry-go-round is a solid 74 kg cylinder of radius of 2 . 3 m. Answer in units of rad / s. 024(part2of2)10.0points What is the change in kinetic energy due to this movement? Answer in units of J. 025 10.0points A 87 . 1 kg man sits on the stern of a 6 . 7 m long boat. The prow of the boat touches the pier, but the boat isn’t tied. The man notices his mistake, stands up and walks to the boat’s prow, but by the time he reaches the prow, it’s moved 5 . 36 m away from the pier. Assuming no water resistance to the boat’s motion, calculate the boat’s mass (not count- ing the man). Answer in units of kg.