d2 d1 As shown in the diagram above, a yellow cart of mass 2.55 kg rolls without friction on an inclined plane. The cart starts with a speed of 3.79 m/s, located a distance d1 = 1.87 meters from the higher end of an ideal spring (which is at its equilibrium length). The plane is inclined at an angle of theta = 0 = 33.3 degrees above horizontal. The ideal spring has a spring constant of 268 newtons per meter. The cart will roll a distance d1 before coming into contact with the spring, and it will continue to compress the spring a distance d2 before instantaneously coming to a stop (when the spring is at its maximum compression) and then moving back up the inclined plane. Assume the only forces acting on the block are normal forces from the plane and the spring, kinetic friction with the surface of the plane, and gravity (with g = 9.81 m/s2). Calculate the distance d2 (in units of meters). 12

d2 d1 As shown in the diagram above, a yellow cart of mass 2.55 kg rolls without friction on an inclined plane. The cart starts with a speed of 3.79 m/s, located a distance d1 = 1.87 meters from the higher end of an ideal spring (which is at its equilibrium length). The plane is inclined at an angle of theta = 0 = 33.3 degrees above horizontal. The ideal spring has a spring constant of 268 newtons per meter. The cart will roll a distance d1 before coming into contact with the spring, and it will continue to compress the spring a distance d2 before instantaneously coming to a stop (when the spring is at its maximum compression) and then moving back up the inclined plane. Assume the only forces acting on the block are normal forces from the plane and the spring, kinetic friction with the surface of the plane, and gravity (with g = 9.81 m/s2). Calculate the distance d2 (in units of meters). 12

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter2: Vectors

Section: Chapter Questions

Problem 77AP: Show that when A+B=C then A2+B2+2ABcos , where is the angle between vectors A and B .

See similar textbooks

Similar questions

Two blocks with masses m1 = 5 kg and m2 = 15 kg are connected by a rope as shown. Thehorizontal surface is smooth and the pulley is weightless and frictionless. If the block starts fromrest, what is the speed of m2 after it has fallen by 6 m. Ans. 9.40 m/s
Conservation of Energy, Projectile Motion, Acceleration x, y, z. A marble of weight=5lb is launch thanks to a spring on a ramp. The spring has a coefficient of rigidity of = 5lb/ft, an unstretched length of s0=7ft. The ramp is 1=9ft long and h=5ft tall. k www. е VA h Th max Range If the velocity at A is vA=9ft/s find: 1. The displacement of the spring needed to reach this velocity. 2. The range of the flight. 3. The maximum altitude of the flight. с In the box below, enter the maximum altitude of the flight in ft with 2 decimals (Question3).
A 2 kg Box slides down an inclined plane. It has an incline of 1.09956 radians and coefficient of kinetic friction of 0.49. What is the final speed of the Box if it started at rest and the change in height is 2.4 m?
A light, rigid rod is 77.0 cm long. Its top end is pivoted on a frictionless, horizontal axle. The rod hangs straight down at rest with a small, massive ball attached to its bottom end. You strike the ball, suddenly giving it a horizontal velocity so that it swings around in a full circle. What minimum speedat the bottom is required to make the ball go over the top of the circle? Answer : 5.49 m/s
A simple pendulum, consisting of a lightweight 25-cm rod and a small 500-g weight, pivotsfrom point P and swings back and forth. At the bottom of its circular trajectory, its speed is 16 cm/s. What is the acceleration of the weight at that point?
A simple pendulum, consisting of a mass of 8.691 kg, is attached to the end of a 3.23 m length of string. If the mass is held out horizontally, and then released from rest, the speed of the mass (in m/s) at the bottom of the swing is:
A cart of mass m, = 6.7 kg is on an inclined ramp (ø = 34.1 degrees). It is attached to a string of negligible mass that goes over an ideal pulley. The other end of the string is attached to another block of mass m, = 11.9 kg, as shown below. The wheels on the cart are good enough that friction between the cart and the ramp is negligible. If the blocks are given an initial speed of v, = 9.1 m/s (with m, moving down the plane), what is the common magnitude of the acceleration of the blocks? (in m/s^2)
A 3.0-hp motor pulls a mini elevator up at constant speed. The elevator has amass of 12.0 kg and starts from the ground. What is the height of the elevatorafter 7.0 s?
Jeff of the Jungle swings on a 7.6-m vine that initially makesan angle of 37° with the vertical. If Jeff starts at rest and has amass of 78 kg, what is the tension in the vine at the lowest pointof the swing?
Two blocks initially at rest, each having a mass of 20 kg, are connected by a string as shown in the figure. The coefficient of sliding friction between the block and the inclined plane is 0.28. The plane is inclined at 350 with the horizontal. The blocks are accelerating at a magnitude of 0.8 m/s2. Assuming the pulleys to be light and frictionless. If the work due to force of friction at B is -105.84 J, find: g. The work done by the Tension at A. (Ans. -154.41 J) h. The work done by the Force of Friction at A. (Ans. -134.86 J) В
Two blocks initially at rest, each having a mass of 20 kg, are connected by a string as shown in the figure. The coefficient of sliding friction between the block and the inclined plane is 0.28. The plane is inclined at 350 with the horizontal. The blocks are accelerating at a magnitude of 0.8 m/s2. Assuming the pulleys to be light and frictionless. If the work due to force of friction at B is -105.84 J, find: a. The displacement moved by the block. (Ans. -3.0 m) b. The work done by the Normal force at B. (Ans. O J) c. The work done by the Gravitation force at B. (Ans. O J) d. The work done by the Tension at B. (Ans. 154.41 J) e. The work done by the Normal force at A. (Ans. 0 J) f. The work done by the Gravitation force at A. (Ans. 337.26 J) g. The work done by the Tension at A. (Ans. -154.41 J) h. The work done by the Force of Friction at A. (Ans. -134.86 J) A В NEER OF
Two blocks initially at rest, each having a mass of 20 kg, are connected by a string as shown in the figure. The coefficient of sliding friction between the block and the inclined plane is 0.28. The plane is inclined at 350 with the horizontal. The blocks are accelerating at a magnitude of 0.8 m/s2. Assuming the pulleys to be light and frictionless. If the work due to force of friction at B is -105.84 J, find: d. The work done by the Tension at B. (Ans. 154.41 J) e. The work done by the Normal force at A. (Ans. 0 J) f. The work done by the Gravitation force at A. (Ans. 337.26 J) A B