Physics 101 Homework

Physics 125 HW5 Assigned Feb. 26; Due Mar. 4, 2020 1. Consider the three masses connected as shown below. The inclined plane makes an angle q with the horizontal and the coefficient of kinetic friction for all surfaces is µk. The pullies are massless and frictionless. The mass m1 moves downward as shown. Answer the following questions.

a) Draw the free body diagrams for each of the masses. b) Apply Newton's second law to each of the masses. DO NOT solve the equations yet. Just set them up. c) Solve your equations in part b) for the acceleration of the system. Your expression for the acceleration should only contain m1 , m2, m3, q, µk, and various constants. 2. Three blocks are being pulled to the right by a 100 N force. Find the tensions in each string connecting the masses. Assume that the surface is frictionless. You may find it easiest to start by drawing the free body diagram of the entire system.

3. Mass m is held against a wall by the force

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Fpush . Mass m does not slide along the wall. The coefficient of static friction between the wall and mass m is

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µS . What is the smallest value of

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Fpush that can be applied so that mass m remains at rest? Your answer will be in the form of an expression.

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100 N

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3 kg

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4 kg

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5 kg

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Wall

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m

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Fpush

4. A circular curve of highway is designed for traffic traveling at 60 km/h (37 mi/h). a) If the radius is 150 m (490 ft), what is the correct angle of banking of the road? b) If the road was not banked, what would be the minimum coefficient of static friction between the tires and the road to keep the cars from sliding using the speeds in part a)? 5. A 150 lb student has an apparent weight of 110 lb at the top of a Ferris wheel that is rotating at a constant angular velocity. (The apparent weight is the normal.) a) What is the student’s apparent weight at the bottom of the Ferris wheel? b) If the speed of the Ferris wheel were doubled, what would be the student’s apparent weight at the top of the Ferris wheel? 6. If the coefficient of static friction for the tires on a road of 0.25, at what maximum speed can a car travel around a horizontal circular road of radius 48 m? 7. Two masses are connected by strings. Each string is 1 m long. Each mass, which is 10 kg, is rotated in a vertical circle. The speed of the top mass is 8 m/s while the speed of the lower mass is 4 m/s. Find the tension in each string. Do not neglect gravity.

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1 m

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8 m/s

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4 m/s

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1 m

8. A 5 kg mass is swung in a vertical circle of radius 2 m. Assume for simplicity that the speed is a constant and equal to 10 m/s. Draw and find the magnitude of the TOTAL, i.e. not just radial, acceleration vector at points A, B, and C.

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R

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v

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θ

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A

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B

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C