A 1 kilogram bead moves with constant total mechanical energy on a frictionless wire track. The track is in a vertical plane and consists of straight segments and circular segments. For example, points B, F, G, H are on straight segments. Points A, C, D, E are on circular track segments. Point A is at the top of the track and point H is the lowest point of the track. The bead is shown initially at point C with a velocity 5.6 m/s down as represented by the velocity arrow. The circular portion of track that includes points A, C, D has a radius 3.2 meters. H radius 3.2m Velocity 5.6 m/s Direction Key 1 7
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- A box of mass 4.0 kg hangs by a cable from the ceiling of an elevator. The elevator is moving up at a steady speed of 5.0 m/s for 8.0 m. Use g = 10 m/s2. Consider the system is the box and the Earth. When apply the following energy principle, considering the system is box+earth, which of the energy term is positive? Select all apply. ΔK + ΔUg + ΔUsp + ΔEth + ΔEch = WextAs shown in the figure, a 0.490kg object is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x. The force constant of the spring is 450 N/m. When it is released, the object travels along a frictionless, horizontal surface to point A, the bottom of a vertical circular track of radius R = 1.00 m, and continues to move up the track. The speed of the object at the bottom of the track is va = 12.8 m/s and the object experiences an average frictional force of 7.00 N while sliding up the track. (a) What is x? (b) If the object were to reach the top of the track, what would be it’s speed at that point? (c) Does the object actually reach the top of the track, or does it fall off before reaching the top?A 26 kg object is acted on by a conservative force given by F = (-2.9)x + (-5.9)x2, with F in newtons and x in meters. Take the potential energy associated with the force to be zero when the object is at x = 0. What is the potential energy of the system associated with the force when the object is at x = 2.0 m? If the object has a velocity of 5.5 m/s in the negative direction of the x-axis when it is at x = 5.0 m, what is its speed when it passes through the origin?
- (a) Part (a) refers to the figure below. A block of mass m = 0.1 kg is going down and inclined plane with an initial speed v₁. The inclined plane makes an angle = 30° with the horizontal and the inclined plane has a kinetic friction coefficient k 0.7. After travelling a distance L = 0.8 m, the block encounters a spring with a spring constant k 20 N/m. The block comes to rest after compressing the spring an amount x = 0.3 m. What is vi, the initial speed of the block? = x = 0 oooo 0 Initial x=0 momo 0 x Initial μk 1 Vi m Mk Part a (b) Part (b) refers to the figure below. The block then goes up the inclined plane again. After the block travels a distance x, the block leaves the spring. The block continues to go up the inclined plane and the block comes to rest after it travels a distance d past the equilibrium position for the spring. What is the distance d? x=0 Part b t 0 x=0 Final 0000 Ө μk Final MkA mass of 10.0 kg is attached to a spring on a frictionless horizontal surface. The spring constant k = 504 Newtons/meters. The spring is stretched until the Potential Energy of the spring is 2.52 Joules. What is the displacement ( in meters) in the spring?The potential energy of a particle as a function of position will be given as U(x) = A x2 + B x + C,where U will be in joules when x is in meters. A, B, and C are constants. What is the force on this particle, in newtons, at x+39cm, if the constants are A= 2.2 J/m^2 , B= 2.2 J/m, and C=6.5 J?
- The only force acting on a 4.0 kg body as the body moves along an x axis varies as shown in the figure. The scale of the figure's vertical axis is set by F = 8.0 N. The velocity of the body at x = 0 is 8.0 m/s. (a) What is the kinetic energy of the body at x = 5.0 m? (b) At what value of x will the body have a kinetic energy of 65.0 J? (c) What is the maximum kinetic energy of the body between x = 0 and x = 5.0 m? F, (N) FN 3 4 x (m) -F,A raindrop of mass 3.20 x 10-5 kg falls vertically at constant speed under the influence of gravity and air resistance. Model the drop as a particle. (a) As it falls 80 m, what is the work done on the raindrop by the gravitational force? J (b) What is the work done on the raindrop by air resistance? JQUESTION 8 OK, same sort of track, but now with d = 2.10 m. Now suppose the blocks starts on the track at x = 4.76 m. The block is given a push to the left and begins to slide up the track, eventually reaching its maximum height at x = 0, at which point it turns around and begins sliding down. What was its initial speed in this case? A 8.30 m/s B 14.55 m/s C 10.29 m/s D 17.39 m/s
- A 1 kilogram bead moves with constant total mechanical energy on a frictionless wire track. The track is in a vertical plane and consists of straight segments and circular segments. For example, points B, F, G, H are on straight segments. Points A, C, D, E are on circular track segments. Point A is at the top of the track and point H is the lowest point of the track. The bead is shown initially at point C with a velocity 5.6 m/s down as represented by the velocity arrow. The circular portion of track that includes points A, C, D has a radius 3.2 meters. 1 2 The "direction key" shows eight arrow directions labeled 1 to 8. To use the "direction key", consider the vector mentioned in each question. Match the direction of the vector with the arrow in the key that best shows the direction of the required vector. st radius 3.2m For example the velocity vector at point C is best represented by arrow "5" in the key. 6 D Determine the direction of the acceleration of the bead at point D. (Use…A block is displaced vertically by Ar = 2.5 m under the influence of three forces, F = 4.0 N, FR = 6.0 N, and F = 8.0 N as shown in the diagram. The angles 0c = 15°. There are no other forces acting on the block. What is the net work done by these three forces on the block? FB %3D %3D %3D 0c FA W = FArcos(0)The figure sows a block and track system. All locations indicated by solid black lines are frictionless. Tan has line is a patch of friction with coefficient ?k = 0.360 whose length is d = 1.45 meters. The small block m has a mass of 0.58 kg and is initially sliding with a speed of v1 = 3.59 m/sec on the raised surface with a height og y1 = 0.532 m. The spring has a spring constant of k = 25.1 N/m.