Circular Motion A1 Kg bead is confined to move on a vertical circle of radius 2 meters. There is no friction between the bead and the circular track. The bead has a speed of 10 m/s when at the top of the circle at point "A", and the total mechanical energy of the bead is assumed to be constant as it moves around the circle. Assume it takes the bead 0.62 seconds to go counter-clockwise from point "A" to point "B" each cycle. 10 m/s 2m 30° Note: vector directions should be given as the "standard" angle with 0 <0 < 360 degrees Calculate the magnitude of the average velocity (m/s) from "A" to "B" (based on the 0.62 seconds mentioned in the description).
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- A 74 kg skier has a speed of 9.2 m/s at point A. She then encounters a 1.75 m deep dip in the snow's surface that has a circular cross section with a radius of curvature of 12 m. Note: You may ignore friction in this problem. a.) How large is the normal force exerted by the snow on the skier at point B? N b.) How much work is done by the normal force on the skier from point A to point B? J 1.75 m r = 12 mA child starts at rest and slides down a frictionless slide as in picture. The bottom of the track is a height h above the ground. The child then leaves the track horizontally, stiking the ground at a distance d as shown. a) Using conservation of energy, find the speed the child at the end of the slide b) Using your answer to part(a) and the equation related to a projectile, determine the initial height H of the child above the ground in terms of h and d2. An ocean diver swims upwards against the drag force exerted by the water. This force varies in magnitude by depth (d) and is given by F(d)=√d, where y=100 N/m ¹/2. If the diver ascends from a depth of d=10m to the surface (d=0), what is the work done by this drag force? Why is this work negative?
- Circular Motion A 1 Kg bead is confined to move on a vertical circle of radius 2 meters. There is no friction between the bead and the circular track. The bead has a speed of 10 m/s when at the top of the circle at point "A", and the total mechanical energy of the bead is assumed to be constant as it moves around the circle. Assume it takes the bead 0.62 seconds to go counter-clockwise from point "A" to point "B" each cycle. 10 m/s 2 m 30° Note: vector directions should be given as the "standard" angle with 0≤0 < 360 degrees Calculate the average speed (m/s) from "A" to "B" (based on the 0.62 seconds mentioned in the description).A 260 g particle in a semi-spherical bowl of radius 0.6 m is released from rest at point A at the level of the center of the bowl, and the surface of the bowl is rough. The speed of the particle at B is 2 m/s. The acceleration of gravity is 9.8 m/s2 . a)What is its kinetic energy at B? b)What is the magnitude of the energy lost due to friction as the particle moves from A to B?c) Eddy and his skateboard with mass a of 65 kg ride on a rough horizontal road as shown in Figure 3. At the bottom of an incline, his velocity is 4 m s1. He rides up the incline and reaches the top with a velocity of 1 m s. The difference in height between the top and the bottom of the incline is 0.6 m. 1 m/s 4 m/s 0.6 m Figure 3 Calculate: i. the total energy of Eddy before he rides on the inclined plane, ii. the total energy of Eddy after the rode up the inclined plane, and ii. the net energy loss due to the friction on the inclined plane. (5 marks)
- A spherically symmetric ball of mass m and radius R is centered at the origin. A thin rod has a mass M uniformly distributed along its length L and lies along the x-axis as shown in the figure below. Determine the gravitational potential energy of the system if U = 0 at x = ∞. y L M тA 500 kg cart rests atop a hill 30.0 m high on a roller coaster. Its gravitational potential energy is measured relative to the bottom of the hill. The cart then rolls down the hill. Which of these best describes what is happening in this situation? a. the total mechanical energy of the cart is decreasing, the kinetic energy of the cart is increasing, and the gravitational potential energy of the cart is increasing b. the total mechanical energy of the cart is increasing, the kinetic energy of the cart is increasing, and the gravitational potential energy of the cart is increasing c. the total mechanical energy of the cart is increasing, the kinetic energy of the cart is increasing, and the gravitational potential energy of the cart is decreasing d. the total mechanical energy of the cart is increasing, the kinetic energy of the cart is decreasing, and the gravitational potential energy of the cart is increasing e. the total mechanical energy of…2 W S X In a hydroelectric dam, water falls 35 m and then spins a turbine to generate electricity. 3 E D 80 C $ 4 R 888 F V 96 5 T G ^ 6 B ▾ Part A What is AU of 1.0 kg of water? Express your answer with the appropriate units. View Available Hint(s) AU= -340 J Y Submit ▾ Part B ✓ Correct SOLVE: The change in the potential energy of 1.0 kg of water in falling 35 m m is H Suppose the dam is 80% efficient at converting the water's potential energy to electrical energy. How many kilograms of water must pass through the turbines each second to generate 48 MW of electricity? This is a typical value for a small hydroelectric dam. Express your answer in kilograms per second. ▸ View Available Hint(s) m 11s AU, -mgh=-(1.0 kg) (9.8 m/s²) (35 m) = -340 J = = Provide Feedback Submit MacBook Air Previous Answers & 7 N IG] ΑΣΦ | 3-4 U * 8 D-H I M @ JK ( 9 MOSISO DD O I भ ? O L kg/s command F10 P > ; C option + ? T I Next > delete re
- ▾ Part A A system of two objects has AKtot 7 J and AUnt=-3 J. = Vocals Search B N How much work is done by interaction forces? Express your answer in joules. Wint ΜΕ ΑΣΦ Submit Previous Answers Request Answer X Incorrect; Try Again; 3 attempts remaining Part B How much work is done by external forces? Express your answer in joules. Wat ΜΕ ΑΣΦ Submit Request Answer Provide Feedback msi ENTER SHIFT ? J J NO.A 11 g particle is moving to the left at 17 m/s. How much net work must be done on the particle to cause it to move to the right at 45 m/s ? Express your answer to two significant figures and include the appropriate units. µA ? W = Value Units Submit Request Answer Provide Feedback Next >1 2 -D- A block of mass M is released from rest at point 1, as shown in the figure. The block slides without frictional forces along the circular arc but encounters frictional forces as soon as it reaches the horizontal portion of the track at point 2. The block travels a distance D along the horizontal track before coming to rest at point 3. Consider the block-Earth system. In terms of the mechanical energy of the system, which of the following claims is correct, and why? A The system is open, because there is a net force exerted on the block. The system is open, because the block's velocity is zero at points 1 and 3. The system is closed, because there is a net force exerted on the block. D The system is closed, because the block's velocity is zero at points 1 and 3.