A child's toy consists of a m = 45 g monkey suspended from a spring of ss and spring constant k. When the toy monkey is first hung on the sprin m reaches equilibrium, the spring has stretched a distance of x= 17.7 cm he diagram. This toy is so adorable you pull the monkey down an 7.1 cm from equilibrium and release it from rest, and smile with deligh playfully up and down.
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
Conservation and energy Q6: please answer parts a, c, and d. Please explain reasoning for all steps even if minor. Part b is answered as shown.
![Problem 6: A child's toy consists of a m = 45 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 = 17.7 cm,
as shown in the diagram. This toy is so adorable you pull the monkey down an
additional d = 7.1 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 : Anumeric value is expected and not an expression.
k =.
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,
-spring
spring
applied
spring
gravity
applied
F.
-spring
spring
spring
Teravity
gravity
F.
F
gravity
applied
applied
Part (c) Calculate the total potential energy, Epottom, in joules, stored in the stretched spring immediately before you release it. Take the zero of
potential energy at the spring's unstretched position before the monkey is suspended from it.
Numeric : Anumeric value is expected and not an expression.
Epottom =
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, hmay, 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, E1op. in terms of m, x, d,
k, the maximum height above the bottom of the motion, hmax, and the variables available in the palette.
Expression :
Etop =
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, v. 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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