An elevator of mass 1000 kg rests at a level 5 m above the base of an elevator shaft. It is raised to 200 m above the base of the shaft, where the cable holding it breaks. The elevator falls freely to the base of the shaft and strikes a strong spring. The spring is designed to bring the elevator to rest and, by means of a catch arrangement, to hold the elevator at the position of maximum spring compression. Assuming the entire process to be frictionless, and taking g = 9.8m/s2. calculate: a. b. C. d. e. The potential energy of the elevator in its initial position relative to the base of the shaft. f. The work done in raising the elevator The potential energy of the elevator in its highest position relative to the base to the shaft The potential energy of the compressed spring The energy of the system consisting of the elevator and spring: i. at the start of the process, ii. When the elevator reaches its maximum height iii. Just before the elevator strikes the spring iv. After the elevator has come to rest. The velocity and kinetic energy of the elevator just before it strikes the spring.

An elevator of mass 1000 kg rests at a level 5 m above the base of an elevator shaft. It is raised to 200 m above the base of the shaft, where the cable holding it breaks. The elevator falls freely to the base of the shaft and strikes a strong spring. The spring is designed to bring the elevator to rest and, by means of a catch arrangement, to hold the elevator at the position of maximum spring compression. Assuming the entire process to be frictionless, and taking g = 9.8m/s2. calculate: a. b. C. d. e. The potential energy of the elevator in its initial position relative to the base of the shaft. f. The work done in raising the elevator The potential energy of the elevator in its highest position relative to the base to the shaft The potential energy of the compressed spring The energy of the system consisting of the elevator and spring: i. at the start of the process, ii. When the elevator reaches its maximum height iii. Just before the elevator strikes the spring iv. After the elevator has come to rest. The velocity and kinetic energy of the elevator just before it strikes the spring.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A vertical ideal spring, spring constant k, is compressed a distance A. A mass m is placed on top of the spring and then released. a) How high will the mass go? Н y=0 y=0 Answer: b) If instead the force exerted by the spring is given by F= -(ky+b), how high will the mass go?
A block of mass 14.0 kg slides from rest down a frictionless 40.0° incline and is stopped by a strong spring with k = 2.30 ✕ 104 N/m.The block slides 3.00 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest, how far has the spring been compressed?
A 2.00 kg mass on a frictionless incline plane of angle 6 degrees is released and begins sliding down the incline. At the bottom of the incline is a spring (k=70 N/m). If the mass slides 0.30 m along the incline plane before it contacts the spring, how far is the spring compressed by the mass? (round to the nearest hundredth)
A block of mass m is at the top of an inclined plane of length L and angle 0. At the bottom of the plane there is a relaxed spring with spring constant k. (See the figure.) The block is released from rest and slides without friction down the plane. At the bottom of the plane, the block strikes the spring and momentarily comes to rest by compressing the spring by some amount D. (a) Find D in terms of m, k, L, g, and 0. (b) Describe in words what the motion will look like over time.
An 8 kg box moving at 2.0 m/s on a horizontal, frictionless surface runs into a light spring of force constant 75 N/cm. Find the maximum compression of the spring (units =m).
The pulley system below consists of two masses connected by a string of negligible mass through a massless pulley. A spring with constant k is placed so that its equilibrium position is located a distance h below the bottom of mass m2. There is no friction either in the pulley, or between the surfaces of the masses and the platform. When the two masses m₁ and m2 are released from rest, mass m2 begins falling and pulls mass m₁ up the ramp. Find an expression for the maximum compression of the spring d caused by mass m2 when it hits the spring. Your answer should be in terms of the variables given (and g). m2 MW my 0
The magnitude of the force required to compress an imperfect horizontal spring a distance x is given by Fbs = kx +bx^3 where k=120N/m and b=18N/m^3. If you use a 7.5kg block to compress the spring a distance of 1.6m and then let it go, what speed will the block have when it leaves the spring? Assume the surfaces are smooth enough that any frictional forces can be neglected.
In a 30°-rough incline, a 2.15 kg block is initially at rest beside a spring that is compressed by 42 cm as shown in the figure below. The spring has a spring constant of 180 N/m and the coefficient of sliding friction between the incline and the block is 0.32. When the spring is released, (a) how far up the incline (with respect to its initial position) will the block slide before sliding back? (b) What is the speed of the block at the instant it is 0.43 m from its initial position?
A block of mass m is initially at rest at the peak of an inclined plane, which has a height of 6.9 m and makes an angle of θ = 29° with respect to the horizontal. After being released, it is observed to be moving at v = 1 m/s a distance d after the end of the inclined plane as shown. The coefficient of kinetic friction between the block and the plane is μp = 0.1, and the coefficient of friction on the horizontal surface is μr = 0.2. Find the distance d, in meters
A 1.20 kg block slides down a frictionless incline with a slope angle of 42.0°, starting from a height 2.30 m above the bottom of the incline. The incline meets a frictionless horizontal surface, at the end of which is a spring in its equilibrium position (k =460. N/m) used to stop the block. Find the maximum compression of the spring.
A 1.5-kg box is released from rest on a frictionless surface that is sloped at θ = 35◦ above the horizontal.After sliding 1.0 m down the slope, the box transitions smoothly to a rough, horizontal surface, slides forsome distance, and then comes to a stop. If the coefcient of kinetic friction between the box and thehorizontal surface is 0.12, how far along the horizontal surface does the box travel?
A sky diver plans to bungee jump from a tower 74.0 m above the ground. She plans to use a uniform elastic cord, tied to a harness around her body, to stop her fall at a point 11.0 m above the water. Model her body as a particle and the cord as having negligible mass and obeying Hooke's law. In a preliminary test she finds that when hanging at rest from a 5.00 m length of the cord, her body weight stretches it by 1.25 m. She will drop from rest at the point where the top end of a longer section of the cord is attached to the tower. (a) What length of cord should she use? m (b) What maximum acceleration will she experience? m/s²