Problem 6: A child's toy consists of a m = 42 g monkey suspended from a spring ofnegligible mass and spring constant k. When the toy monkey is first hung on the springand the system reaches equilibrium, the spring has stretched a distance of x = 16.1 cm,as shown in the diagram. This toy is so adorable you pull the monkey down anadditional d = 4.1 cm from equilibrium and release it from rest, and smile with delightas it bounces playfully up and down.UnstretchedPositionEquilibriumStretched PositionPart (a) Using the given information, determine the spring constant, k, in Newtons per meter, of the spring.Numeric : A numeric value is expected and not an expression.k =2.557Part (b) Select the free-body diagram that best represents the forces acting on the monkey as you are pulling it down, immediately before you letgo.SchematicChoice :F.AF,springspringspringF.F.Fgravity.FappliedappliedF,A FspringspringF.FoppliedspringFE.gravityF.gravitgravityappliedPart (c) Calculate the potential energy, Epottom, in joules, stored in the stretched spring immediately before you release it.Numeric : A numeric value is expected and not an expression.Epottom =05215Part (d) Assume that the system has zero gravitational potential energy at the lowest point of the motion. Derive an expression for the totalmechanical energy, Eequilibrium- of the system as the monkey passes through the equilibrium position in terms of m, x, d, g, k, and the speed of themonkey, ve-Expression :Eequilibrium =Select from the variables below to write your expression. Note that all variables may not be required.a, B, 0, a, d, g, h,max, i, j, k, m, P, t, ve, XPart (e) Calculate the speed of the monkey, ve, in meters per second, as it passes through equilibrium.Numeric : A numeric value is expected and not an expression.Ve =Part (f) Derive an expression for the total mechanical energy of the system as the monkey reaches the top of the motion, Eop; in terms of m, x, d,k, the maximum height above the bottom of the motion, hmar, and the variables available in the palette.Expression :Etop =mghmax +1)2u (x-d)?Select from the variables below to write your expression. Note that all variables may not be required.a, ß, 0, a, d, g, hmax, i, j, k, m, P, t, ve, xPart (g) Calculate the maximum displacement, h, in centimeters, above the equilibrium position, that the monkey reaches.Numeric : A numeric value is expected and not an expression.h =

Answered: Image /qna-images/answer/e885e427-3cfa-4bb6-ab80-0a9f14ff6a87.jpg

Problem 6: A child's toy consists of a m = 42 g monkey suspended from a spring of | negligible mass and spring constant k. When the toy monkey is first hung on the spring and the system reaches equilibrium, the spring has stretched a distance of x = 16.1 cm, as shown in the diagram. This toy is so adorable you pull the monkey down an additional d= 4.1 cm from equilibrium and release it from rest, and smile with delight as it bounces playfully up and down. Un

Problem 6: A child's toy consists of a m = 42 g monkey suspended from a spring of | negligible mass and spring constant k. When the toy monkey is first hung on the spring and the system reaches equilibrium, the spring has stretched a distance of x = 16.1 cm, as shown in the diagram. This toy is so adorable you pull the monkey down an additional d= 4.1 cm from equilibrium and release it from rest, and smile with delight as it bounces playfully up and down. Un

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)...

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Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

Problem 6: A child's toy consists of a m = 42 g monkey suspended from a spring of
negligible mass and spring constant k. When the toy monkey is first hung on the spring
and the system reaches equilibrium, the spring has stretched a distance of x = 16.1 cm,
as shown in the diagram. This toy is so adorable you pull the monkey down an
additional d = 4.1 cm from equilibrium and release it from rest, and smile with delight
as it bounces playfully up and down.
Unstretched
Position
Equilibrium
Stretched Position
Part (a) Using the given information, determine the spring constant, k, in Newtons per meter, of the spring.
Numeric : A numeric value is expected and not an expression.
k =
2.557
Part (b) Select the free-body diagram that best represents the forces acting on the monkey as you are pulling it down, immediately before you let
go.
SchematicChoice :
F.
AF,
spring
spring
spring
F.
F.
F
gravity
.F
applied
applied
F,
A F
spring
spring
F.
Fopplied
spring
F
E.
gravity
F.
gravit
gravity
applied
Part (c) Calculate the potential energy, Epottom, in joules, stored in the stretched spring immediately before you release it.
Numeric : A numeric value is expected and not an expression.
Epottom =
05215
Part (d) Assume that the system has zero gravitational potential energy at the lowest point of the motion. Derive an expression for the total
mechanical energy, Eequilibrium- of the system as the monkey passes through the equilibrium position in terms of m, x, d, g, k, and the speed of the
monkey, ve-
Expression :
Eequilibrium =
Select from the variables below to write your expression. Note that all variables may not be required.
a, B, 0, a, d, g, h,max, i, j, k, m, P, t, ve, X
Part (e) Calculate the speed of the monkey, ve, in meters per second, as it passes through equilibrium.
Numeric : A numeric value is expected and not an expression.
Ve =
Part (f) Derive an expression for the total mechanical energy of the system as the monkey reaches the top of the motion, Eop; in terms of m, x, d,
k, the maximum height above the bottom of the motion, hmar, and the variables available in the palette.
Expression :
Etop =
mghmax +1)2u (x-d)?
Select from the variables below to write your expression. Note that all variables may not be required.
a, ß, 0, a, d, g, hmax, i, j, k, m, P, t, ve, x
Part (g) Calculate the maximum displacement, h, in centimeters, above the equilibrium position, that the monkey reaches.
Numeric : A numeric value is expected and not an expression.
h =

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