You are working during your summer break as an amusement park ride operator. The ride you are controlling consists of a large vertical cylinder that spins about its axis fast enough that any person inside is held up against the wall when the floor drops away (see the figure below). The coefficient of static friction between a person of mass m and the wall is μs′ and the radius of the cylinder is R. You are rotating the ride with an angular speed ω suggested by your supervisor. (a) Suppose a very heavy person enters the ride. Do you need to increase the angular speed so that this person will not slide down the wall? Yes No (b) Suppose someone enters the ride wearing a very slippery satin workout outfit. In this case, do you need to increase the angular speed so that this person will not slide down the wall? Yes No
(b) Two boxes of mass m1 = m2 = m = 10 kg, attached together with an inextensible string, are pulled across the floor by a girl using another inextensible string that is making an angle of 30∘ with the horizontal, as shown in figure 1. The kinetic friction between each box and the ground is 0.1 and the boxes are accelerating at 2.0 m/s2. T1 and T2 are the tensions in the two inextensible strings. Figure 1: (i) Draw the free-body diagram of each of the boxes. (ii) What is the tension (T1) on the string which is attached to the two boxes? (iii) What is the tension (T2) on the string which is in the hand of the girl?
A variable capacitor with a range from 8.2 to 306 pF is used with a coil to form a variable-frequency LC circuit to tune the input to a radio. (a) What is the ratio of maximum frequency to minimum frequency that can be obtained with such a capacitor? If this circuit is to obtain frequencies from 0.76 MHz to 2.42 MHz, the ratio computed in (a) is too large. By adding a capacitor in parallel to the variable capacitor, this range can be adjusted. To obtain the desired frequency range, (b) what capacitance in picofarads should be added and (c) what inductance should the coil have? (a) Number Units (b) Number Units (c) Number Units
A 100-lb boy at A is suspended from the cable that passes over the quarter circular cliff rock. The coefficient of static friction between the cable and the rock is μs = 0.2, and between the shoes of the woman and the ground μs' = 0.8 Determine if it is possible for the 150−lb woman to hoist him up Write your steps and details, in the space provided with the problem. Listing only the answer (Yes/No) will result in reduced credit
A worker pushed a 28.0 kg block 14.0 m along a level floor at constant speed with a force directed 30.0∘ below the horizontal. If the coefficient of kinetic friction between block and floor was 0.310, what were (a) the work done by the worker's force and (b) the increase in thermal energy of the block-floor system? (a) Number Units (b) Number Units
The 90.0−lb boy at A is suspended from the cable that passes over the quarter circular cliff rock. Determine if it is possible for the 175−lb woman to hoist him up. The coefficient of static friction between the cable and the rock is μs = 0.2, and between the shoes of the woman and the ground μs′ = 0.8. (Figure 1) Figure 1 of 1 Submit Previous Answers Request Answer Part B Determine the maximum possible force due to friction that opposes the motion of the woman. Express your answer to three significant figures and include the appropriate units. Submit Previous Answers Request Answer
A simple harmonic oscillator consists of a block of mass 2.60 kg attached to a spring of spring constant 230 N/m. When t = 1.30 s, the position and velocity of the block are x = 0.151 m and v = 4.060 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s? (a) Number Units (b) Number Units (c) Number Units
In the figure, block A (mass 13.0 kg) is in equilibrium, but it would slip if block B (mass 7.62 kg) were any heavier. For angle θ = 30.1∘, what is the coefficient of static friction between block A and the surface below it? Number Units
Questions 11-14 Consider the track shown in the figure. The section AB is one quadrant of a circle of radius 2.0 m and is frictionless. B to C is a horizontal span that is 3.0 m long with a coefficient of kinetic friction μk = 0.25. The section CD under the spring is frictionless. A block of mass 1.0 kg is released from rest at A. After sliding on the track, it compresses the spring by 0.20 m. Take the gravitational acceleration as g = 10 m/s2 11. What is the velocity of the block at point B? (a) 210 m/s (b) 25 m/s (c) 45 m/s (d) 10 m/s (e) 310 m/s 12. What is the thermal energy produced as the block slides from B to C? (a) 2.5 J (b) 0 J (c) 3 J (d) 5 J (e) 7.5 J 13. What is the the velocity of the block at point C? (a) 10 m/s (b) 5 m/s (c) 4 m/s (d) 2 m/s (e) 6 m/s 14. What is the stiffness constant k for the spring? (a) 625 N/m (b) 250 N/m (c) 750 N/m (d) 25 N/m (e) 500 N/m
Questions 13-16 A string is wound around the rim of a uniform disk that is pivoted to rotate without friction about a fixed axis through its center. The mass of the disk is m = 3 kg and its radius is R = 20 cm. The string is initially at rest and is pulled with a time dependent force F = F0t2 where F0 is given as 10 N/s2.13. What is the moment of inertia of this disk in kg⋅m2? (a) 0.48 (b) 0.12 (c) 0.03 (d) 0.06 (e) 0.24 14. What is the magnitude and direction of torque on the disk at t = 2 s? (a) 8 N⋅m, +x (b) 16 N⋅m, −z (c) 16 N⋅m, +y (d) 8 N⋅m, −x (e) 16 N⋅m, +z 15. What is the magnitude and direction of angular acceleration of the disk at t = 2 s? (a) 800/3 rad/s2, −z (b) 400/3 rad/s2, +x (c) 800/3 rad/s2, +y (d) 400/3 rad/s2, −x (e) 800/3 rad/s2, +z 16. What is the magnitude and direction of the angular velocity of the disk at t = 2 s? (a) 400 rad/s, −x (b) 800/9 rad/s, −x (c) 800 rad/s, +z (d) 800 rad/s, −z (e) 800 rad/s, +y