PHSX 220 Homework 11 Paper – Due Thursday April 13th 5:00 pm Problem 1: In class we watched a video involving a motor cycle and a playground merry-go-round (https://www.youtube.com/watch?v=btxMd5mbPeM). We will consider the two people on the merry-go-round to be 85 kg point masses located at the edge of a 200 kg solid disk with a radius of 1.5m. a) Calculate the moment of inertia for the system of two 85 kg point masses at 1.5 m and a 200 kg solid disk of radius 1.5m b) After 6 seconds of the motorcycle applying a force at the radius of the merry-go-round, the system rotates at 1 revolution per second. Calculate the average force applied by the motorcycle on the system during the six second interval. Hint: Given a time interval and impulse, which is a change in momentum, average forces and torques can be calculated. c) Once the unfortunate person is released (without putting a net torque on the remaining parts of the system), they leave with linear momentum that is tangent to the merry-go-round – thus leaving with angular momentum. Does the remaining person/merry-go-round rotational velocity speed up, slow down or remain the same? Problem 2: A 600 N (mg has been calculated for you) board with a total length of 8 meters is held in static equilibrium by two students and a frictionless pivot point. The pivot point is 6 m from student A on the left. Student B applies a completely horizontal force of 250 N to the left. The person on the right applies a force at an unknown angle, , above the horizontal direction. Answer the following questions in regards to the situation. a) Calculate the x component of the force applied by the person on the left. b) Calculate the y component of the force applied by the person on the left. c) Calculate the magnitude of the force being applied by the person on the left. d) Calculate the angle above the horizontal of the force being applied by the person on the left. e) Calculate the magnitude of the normal force by the pivot on the board. Problem 3: A 10 meter long, 1000 kg drawbridge (uniform board) is held stationary at an angle by the tension of a rope and a hinge located where the board is attached to the wall. a) Calculate the magnitude of the tension in the rope for the conguration shown b) Calculate the magnitude of the force by the hinge on the board in the x direction c) Calculate the magnitude of the force by the hinge on the board in the y direction Problem 4: Shown in the gure below is a 5 meter, 10 kg uniform ladder leaning on a frictionless wall at an angle of 60 degrees to the oor. The COM for the ladder is located half-way up the ladder. The oor has a static coecient of friction equal to 0.42. A person climbs the ladder and above some point the ladder slips out and falls. Calculate the following at the point where the person is at the maximum distance up along the ladder before it slips. a) Calculate the normal force of the oor on the ladder with the person a distance d along the length of the ladder. b) Calculate the normal force of the wall on the ladder with the person a distance d along the length of the ladder. c) Calculate the greatest distance, d, along the length of the ladder a person can climb without the ladder slipping. Problems 5-6: Chapter 12 Problems 28, 30

PHSX 220 Homework 11 Paper – Due Thursday April 13th 5:00 pm Problem 1: In class we watched a video involving a motor cycle and a playground merry-go-round (https://www.youtube.com/watch?v=btxMd5mbPeM). We will consider the two people on the merry-go-round to be 85 kg point masses located at the edge of a 200 kg solid disk with a radius of 1.5m. a) Calculate the moment of inertia for the system of two 85 kg point masses at 1.5 m and a 200 kg solid disk of radius 1.5m b) After 6 seconds of the motorcycle applying a force at the radius of the merry-go-round, the system rotates at 1 revolution per second. Calculate the average force applied by the motorcycle on the system during the six second interval. Hint: Given a time interval and impulse, which is a change in momentum, average forces and torques can be calculated. c) Once the unfortunate person is released (without putting a net torque on the remaining parts of the system), they leave with linear momentum that is tangent to the merry-go-round – thus leaving with angular momentum. Does the remaining person/merry-go-round rotational velocity speed up, slow down or remain the same? Problem 2: A 600 N (mg has been calculated for you) board with a total length of 8 meters is held in static equilibrium by two students and a frictionless pivot point. The pivot point is 6 m from student A on the left. Student B applies a completely horizontal force of 250 N to the left. The person on the right applies a force at an unknown angle, , above the horizontal direction. Answer the following questions in regards to the situation. a) Calculate the x component of the force applied by the person on the left. b) Calculate the y component of the force applied by the person on the left. c) Calculate the magnitude of the force being applied by the person on the left. d) Calculate the angle above the horizontal of the force being applied by the person on the left. e) Calculate the magnitude of the normal force by the pivot on the board. Problem 3: A 10 meter long, 1000 kg drawbridge (uniform board) is held stationary at an angle by the tension of a rope and a hinge located where the board is attached to the wall. a) Calculate the magnitude of the tension in the rope for the conguration shown b) Calculate the magnitude of the force by the hinge on the board in the x direction c) Calculate the magnitude of the force by the hinge on the board in the y direction Problem 4: Shown in the gure below is a 5 meter, 10 kg uniform ladder leaning on a frictionless wall at an angle of 60 degrees to the oor. The COM for the ladder is located half-way up the ladder. The oor has a static coecient of friction equal to 0.42. A person climbs the ladder and above some point the ladder slips out and falls. Calculate the following at the point where the person is at the maximum distance up along the ladder before it slips. a) Calculate the normal force of the oor on the ladder with the person a distance d along the length of the ladder. b) Calculate the normal force of the wall on the ladder with the person a distance d along the length of the ladder. c) Calculate the greatest distance, d, along the length of the ladder a person can climb without the ladder slipping. Problems 5-6: Chapter 12 Problems 28, 30

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