Find the location of the point at which the kinetic energy and the potential energy are equal in terms of the constants of the spring and the body
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- (a) On the grid below, sketch the potential energy of the object-spring-Earth system as a function oftime. Explicitly label any intercepts, asymptotes, maxima, or minima with numerical values, asappropriate. (b) On the axes below, sketch the acceleration of the object as a function of time. Explicitly label anyintercepts, asymptotes, maxima, or minima with numerical values, as appropriate.An ideal sprng Of Go J when Stretched by 5.0cm from epuribrim position. What Š the fariel spring constant) Of the Spring in N/m? has a Potential enercgyInitially sliding with a speed of 4.1 m>s, a 1.5-kg block collideswith a spring and compresses it 0.27 m before coming to rest.What is the force constant of the spring?
- a carriage hits a safety stop at a speed Vo = 3.25 m/s and is completely immobilized by Cinear springs which dece ler ahon expressed -k, x - k2 repres ents compression of the springs starhing from the posihion, and k,. and k, positive cons tanks , Pf the block non of a has cause d by a 3 k, x°, where x the magnitude of the Sprir unde formed kz are maximum com pression of and the the springs speed at the midpoint of is H75`mm deformahion is 2.85 m/s coilculate the constants k, anod le, and ba by spe cifying Hheir units.A bungee cord is essentially a very long rubber bandthat can stretch up to four times its unstretched length.However, its spring constant varies over its stretch [seeMenz, P.G. “The Physics of Bungee Jumping.” The PhysicsTeacher (November 1993) 31: 483-487]. Take the length ofthe cord to be along the x-direction and define the stretchx as the length of the cord l minus its un-stretched lengthl0; that is, x = l − l0 (see below). Suppose a particularbungee cord has a spring constant, for 0 ≤ x ≤ 4.88 m , ofk1 = 204 N/m and for 4.88 m ≤ x , of k2 = 111 N/m.(Recall that the spring constant is the slope of the forceF(x) versus its stretch x.) (a) What is the tension in thecord when the stretch is 16.7 m (the maximum desired for agiven jump)? (b) How much work must be done against theelastic force of the bungee cord to stretch it 16.7 m?A block of mass m and speed v collides with a spring,compressing it a distance ∆x. What is the compression of thespring if the force constant of the spring is increased by a factorof four?
- The torce reguired to compress a non-standard spring as a qunction as. 04 displacement isgiven by the equation F(X) = -Asin (bx)t Kx, where A= 1L0N, b= 1l rad|m, and k- 58 NIm.0 IE M Part A:Enter a general equation in terms 07 the given I iiar 1iaNariables 7or the work requircol to comeress this spring7om positionx, txa: part Bi calculate the work done injouicr as the spring Is come ressed prmi itt bot Woe1=? Arom x=0t X,=38 cm. joulEJ asthe Spring Is Partc: calculate the Workdone in compressed 7rom x1=38cm To xg=69 cmAn ideal spring can compress 2.33 cm by a force of 555 N, a block of mass m = 3.18 kg is released from rest on an inclined plane, the onclination of the plane is 32 degrees, the block rest momentarly when the spring is compress 5.48 cm. Find the distance d that the block travels from the begining of the motion until it reaches the spring. (g = 10 m/s2 ).What is the maximum speed vmax of the block during this motion? Find the acceleration a of the block as a function of time. Find Kmax, the maximum kinetic energy of the block.
- A bungee cord is essentially a very long rubber band that can stretch up to four times its unstretched length. However, its spring constant vanes over its stretch [see Menz, P.G. “The Physics of Bungee Jumping.” The Physics Teacher (November 1993) 31: 483-487]. Take the length of the cord to be along the direction and define the stretch as the length of the cord minus its un-stretched length that is, (see below). Suppose a particular bungee cord has a spring constant, for of and for. (Recall that the of (Recall that the spring constant is the slope of the force versus its stretch (a) What is the tension in the cord when the stretch is 16.7 m (the maximum desired for a given jump)? (b) How much work must be done against the elastic force of the bungee cord to stretch It 16.7 m? Figure 7.16 (credit modification of work by Graeme Churchard)A student working on a school project modeled a trampoline as a spring obeying Hookes law and measured the spring constant of a certain trampoline as 4617 N/m. If a child of mass 27.0 kg compresses the trampoline vertically by a maximum of 0.25 m, while bouncing up and down, what is the childs acceleration at the moment of maximum compression?In an iconic movie scene, Forrest Gump (https://openstaxcollege.org/l/21ForrGumpvid) runs around the country. If he is running at a constant speed of 3 m/s, would it take him more or less energy to run uphill or downhill and why?
