Statics in the human body
.pdf
keyboard_arrow_up
School
Temple University *
*We aren’t endorsed by this school
Course
1061
Subject
Mechanical Engineering
Date
Apr 3, 2024
Type
Pages
6
Uploaded by DeaconSharkMaster285
T E M P L E U N I V E R S I T Y P H Y S I C S 3/14/2024 1:31 PM 1 Statics in the human body The human body is truly an amazing machine, and it can be understood, in part, using the concept of static equilibrium. An object in static equilibrium isn’t accelerating or rotating, which means that all the torques and forces acting on the object must sum to zero: ∑ ࠵?⃗ = 0
∑ ࠵?
⃑
= 0
In principle, a given force could produce both translation and
rotation. The torque produced by a force ࠵?
is defined in vector form by the equation ࠵?⃗ = ࠵?⃗ × ࠵?
⃗
. In this lab we’ll concern ourselves with only the magnitude of the torque, thus simplifying the equation to ࠵? = ࠵?࠵? sin θ
. (Equation 1) The diagram below defines the terms in Equation 1. The lever arm ࠵?
is the line connecting the pivot and the point of application of the force. The angle θ
is the angle between the force and the lever arm. Learning goals for this lab: •
Understand the conditions for static equilibrium when both force and torque are acting. •
Show how joints in the body can be modeled by simple levers. •
Derive the relations showing mechanical advantages and disadvantages of levers. Apparatus: pivot stand, meterstick, pivot bolt and wingnut, 2 sliding mass hangers, 500 g mass, wireless force sensor.
Part I. Standing on tiptoes: the class II lever
A class II lever is one where the load and the applied force are on the same side of the fulcrum, but the load is closer to the fulcrum than the applied force. Two examples of the class II lever are the foot standing on tiptoes and the wheelbarrow, as shown in Figure 1 below. θ
࠵?
࠵?
T E M P L E U N I V E R S I T Y P H Y S I C S 3/14/2024 1:31 PM 2 a.
Set up your apparatus as in the photo above. To do this, turn on the force sensor and open the Capstone software. In the hardware setup menu, click on your force sensor (if multiple sensors appear, identify yours using the ID no. on the sensor). From the display option menu at right, make a digits display of the force as well as a graph of force vs. time. Click Record
to see live data, then without any force acting on it, zero the force sensor using the zero button at the bottom of the screen that looks like this: b.
Weigh and record the mass of the meterstick for later (the mass will be needed in Part III). Then mount the meterstick in the stand at the fifth hole from the bottom as in the photo above by slotting the meterstick into the stand then passing the pivot bolt through the holes in the stand and the 1 cm mark of the meterstick. Secure the pivot bolt using the wingnut provided. c.
Slide the blue mass hangers onto the meterstick as in the photo above, making sure the second hanger is inverted so the force sensor can be hooked onto it. Hook the 500 g weight on the first hanger (the total weight of the load is 510 g since the mass hanger is 10 g). pivot force sensor mass hangers 500 g mass
T E M P L E U N I V E R S I T Y P H Y S I C S 3/14/2024 1:31 PM 3 d.
Carry out a quick observation on how the location of the load affects the force that must be applied to maintain equilibrium (the precise values of force and position are not important). To do this, apply force by pulling up on the force sensor as in the photo below until the 510 g load is lifted a few millimeters off the benchtop and the meterstick is horizontal. Keep the meterstick horizontal while you vary the lever arm of the 510 g load by sliding it back and forth as shown below. Observe how the force you apply must change for short load lever arms as compared to long load lever arms. For the data section of your report, record your observation as to how the applied force must change as you move the load farther from the pivot. Question 1.
In the observation you just made, the meterstick was in static equilibrium. Thus, there was zero net torque on the meterstick and the counterclockwise torque was equal to the clockwise torque. Sketch a free-body diagram that shows the pivot and the meterstick and label the applied force ࠵?
A
and lever arm ࠵?
A
as well as the load force ࠵?
L
and its lever arm ࠵?
L
. Then, starting with the torque equilibrium equation below, derive an expression for the applied force ࠵?
A
in terms of the lever arms ࠵?
A
and ࠵?
L
and the weight of the load ࠵?
L
. Assume that θ
A
and θ
L
equal 90 degrees. ∑ ࠵?⃗ = ࠵?
A
− ࠵?
L
= ࠵?
A
࠵?
A
sin θ
A
− ࠵?
L
࠵?
L
sin θ
L
= 0
(Equation 2) Question 2.
Class II levers like ankles and wheelbarrows are useful because they provide mechanical advantage
, by amplifying the input force to provide a greater output force. Use your derived expression from Question 1 to show that the applied force needed will always be less than the weight of the load for class II levers. e.
In your experiment, where should the two forces be located to obtain the greatest possible mechanical advantage? Slide the forces to the locations where you obtain the greatest mechanical advantage and apply force via the force sensor. Record the values for ࠵?
A
and ࠵?
L
noting that the pivot is at the 1 cm mark so you must subtract 1 cm from the meterstick readings. Use your values of ࠵?
A
and ࠵?
L
to calculate the mechanical advantage as a multiplicative factor. Record the values for your lab report. A final note on Part I. As you saw, the lever amplifies our input force, but we know from energy conservation that the energy input must equal the energy output. So, what is exchanged in order to obtain the force increase? Displacement. When you lift the load, you can see that the vertical displacement of your hand is much greater than the vertical displacement of the load. Vary the load’s lever arm by sliding it along the meterstick.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Related Questions
Each time your heart beats, your blood pres-
sure first increases and then decreases as the heart rests
between beats. The maximum and minimum blood pressures
are called the systolic and diastolic pressures, respectively.
Your blood pressure reading is written as systolic/diastolic.
A reading of 120/80 is considered normal.
A certain person's blood pressure is modeled by the function
p(1) = 115 + 25 sin(16071)
where p(t) is the pressure in mmHg (millimeters of mer-
cury), at time t measured in minutes.
Find the blood pressure reading. How does this
compare to normal blood pressure?
arrow_forward
Mechanical EngineeringFluid Mechanics
arrow_forward
References:
1-J.L Meriam and L. G. Kr.
2012.
C. Hibbeler, Engineering Mecha
tice Hall 2004,
and E. R. Johnston, 'Vector Mec.
ENGINEERING MECHANICS STATICS
Example 6\ The t-component of the force F is known to be 75 N. Determine the n
component
and the magnitude of F.
72
F.
10°
30°
arrow_forward
Q1 A and B
arrow_forward
1:19 P
N{ l 100% I
A docs.google.com
A block of mass m = 2 kg is attached to a
spring with spring constant k = 200 N/m,
and is set to oscillate on a friction-less
horizontal surface. At time t = 0 its position
is xO = 0 and its velocity is vo = +5 m/s. If
the displacement is a cosine function,
x(t)=A cos(wt+p), then which answer is
correct about the oscillation amplitude A
and the phase constant,p,:
A = 0.25 m, and p = - T/2
A = 0.5 m, p = 0
A = 0.5 m, and p = r/2
A = 0.5 m, p = -T/2
A = 0.25 m, and p = t/2
Other:
A body oscillates with simple harmonic
frictionless motion along the x-axis. Its
displacement varies ith time according to
x(t)=0.5 cos(Tt). The
ues of the velocity
(in m/s) and acceleration (in m/s^2) of the
8
II
arrow_forward
Please solve this question in handwriting step by step. Again Please in handwriting.
arrow_forward
Q3/ In real life engineering application, it is required to design a spring in train, which one of
the following materials in the table below should be choose, justify your answer ? used correct
units?
Poisson's
Yield Strength
Modulus of Elasticity
106 psi
Material
MPа
psi
GPa
Ratio
30
0.30
120000
207
Steel alloy
Brass alloy
Aluminum alloy
Titanium alloy
830
0.34
0.33
380
55000
97
14
275
40000
69
10
690
100000
107
15.5
0.34
arrow_forward
A mechanic is trying to tighten a giant bolt using a wrench. Forces are applied at points A and B.
d₁
0₁
160 N
570 N
15 degrees
15 degrees
40 degrees
0.35 m
0.19 m
F₁
clockwise
N-m
Which direction is Mo rotating?
counter-clockwise
d2
A
0₂
Values for the figure are given in the following table. Note the figure may not be to scale.
Variable Value
F₁
03
X
F₂
0₁
0₂
03
d₁
d₂
a. Using Varignon's Theorem, determine the magnitude of the moment about the origin, Mo.
Round your final answers to 3 significant digits/figures.
Mo=
F2
arrow_forward
PHYS X PHYS X
印 PHYS X
PHYS X
POTPHYS X
PHYS X
E PHYS X E PHYS
top/semester2/physics%20for%20engineers/PHYS220_CH15_Lecture%20Notes_Problems%2015 19,15.29 S
(D Page view
A Read aloud
V Draw
Problem-15-19: page-475
A 0.500-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion
with an amplitude of 10.0 cm. Calculate the maximum value of its
(a) speed, and acceleration.
(b) the speed and the acceleration when the object is 6.00 em from the equilibrium position, and
(c) the time interval required for the object to move from.r50 to r5 8.O0 cm.
Solution:
arrow_forward
Thermodynamics
Topic: Ideal Gas or Perfect Gas
Solve completely in handwritten with given, req’d & sol’n
Thank you!
arrow_forward
THERMODYNAMICS
TOPIC: FIRST LAW OF THERMO/THERMODYNAMIC SYSTEM
PLEASE ANSWER COMPLETELY THE QUESTION IN HANDWRITING AND SUPPORT YOUR SOLUTION WITH DIAGRAMS.
THANK YOU
arrow_forward
Solve the problem quick & carefully On a sheet of paper with FBD , Don't copy which might be wrong.
arrow_forward
Need help, round answers to 3 sig figs please
arrow_forward
APPLICATIONS OF FIRST ORDER DIFFERENTIAL EQUATIONS
Newton’s Law of Cooling and Joint Proportions
At 4:00pm, a thermometer reading of 28 deg C is taken outside where the ambient temperature is –11 deg C. At 4:05 pm, the thermometer reads 8 deg above zero. After a while, the thermometer is returned to the room maintained at 28 deg C. At 4:12pm, the thermometer reads 15 deg C. When was the thermometer returned to the room?
arrow_forward
I need the answer as soon as possible
arrow_forward
is a mass hanging by a spring under the influence of gravity. The force due to gravity, Fg, is acting
in the negative-y direction. The dynamic variable is y. On the left, the system is shown without spring deflection.
On the right, at the beginning of an experiment, the mass is pushed upward (positive-y direction) by an amount y₁.
The gravitational constant g, is 9.81 m/s².
DO
C.D
Frontly
у
Your tasks:
No Deflection
m
k
Fg = mg
Initial Condition
y
m
k
Write down an expression for the total energy If as the sum
Write down an expression for the total energy H
Fg = mg
Figure 3: System schematic for Problem 4.
Yi
&
X
Write down, in terms of the variables given, the total potential energy stored in the system when it is held in
the initial condition, relative to the system with no deflection.
as the sum of potential and kinetic energy in terms of y, y, yi
C After the system is released, it will start to move. Write down an expression for the kinetic energy of the
system, T, in terms of…
arrow_forward
Please try to answer the question within 25-30 minutes
arrow_forward
2:41
.ll ?
a docs.google.com
answer all questions
The number of oscillations completed by
simple pendulum in one second is called? *
Amplitude
Time period
Frequency
Wavelength
Two pendulums of the same length are set
up. If one bob is heavier than the other,
what is the period of oscillation of the
pendulum of the heavier bob? *
Remains the same.
Greater or same as the lighter bob.
Lesser than the lighter bob.
Greater than the lighter bob.
Relative to its period on the earth, the
period a pendulum on the moon(1.625 m/s2)
is *
The same as on the earth
arrow_forward
Determine the equivalent spring stiffness constant of the following.
arrow_forward
is a mass hanging by a spring under the influence of gravity. The force due to gravity, Fg, is acting
in the negative-y direction. The dynamic variable is y. On the left, the system is shown without spring deflection.
On the right, at the beginning of an experiment, the mass is pushed upward (positive-y direction) by an amount y₁.
The gravitational constant g, is 9.81 m/s².
No Deflection
m
k
Fg = mg
Initial Condition
m
k
Fg = mg
Figure 3: System schematic for Problem 4.
Yi
8
Your tasks:
A Write down, in terms of the variables given, the total potential energy stored in the system when it is held in
the initial condition, relative to the system with no deflection.
B Write down an expression for the total energy H as the sum of potential and kinetic energy in terms of y, y, yi
and element parameters. Will H change as the mass moves?
C After the system is released, it will start to move. Write down an expression for the kinetic energy of the
system, T, in terms of position, y, the initial…
arrow_forward
THERMODYNAMICS
arrow_forward
I need help with 10
arrow_forward
1. For your science fair project, you decided to design a model rocket ship.
The fuel burns exerting a time-varying force on the small 2.00 kg rocket
model during its vertical launch. This force obeys the equation F= A + Bt2.
Measurements show that at t=0, the force is 25.0 N, and at the end of the
first 2.00 s, it is 45.0 N. Assume that air resistance is negligible.
a. What are the forces acting on the rocket?
b. Draw its free-body diagram.
c. Find the constants A and B, including their SI units using this
equation F= A + Bt².
d. Find the net force on this rocket and its acceleration the instant after
the fuel ignites.
e. Find the net force on this rocket and its acceleration 3.00 s after fuel
ignition.
f. Suppose you were using this rocket in outer space, far from all gravity.
What would its acceleration be 3.00 s after fuel ignition?
g. What is the rocket's mass in outer space? What is its weight?
arrow_forward
THERMODYNAMICS
TOPIC: FIRST LAW OF THERMO/THERMODYNAMIC SYSTEM
PLEASE ANSWER COMPLETELY THE QUESTION IN HANDWRITING AND SUPPORT YOUR SOLUTION WITH DIAGRAMS.
THANK YOU
arrow_forward
4. For a particular thermocouple, if one junction is maintained at 0°C (cold junction) and the other junction is used as
a probe to measure the desired Celsius temperature t, the voltage V generated in the circuit related to the
temperature t as
V = t (a + bt)
Further, for this thermocouple, when V is in millivolts, the two constants are a = 0.25 and b = -5.5 x10+. Determine
the value of V if the measured temperature is 100°C.
arrow_forward
4- A thermometer having a time constant of 0.4 min. is placed in a temperature bath and after the
thermometer comes to equilibrium with the bath, the temperature of the bath is increased linearly
with time at the rate of 2 deg.C min. what is the difference between the indicated temperature and
bath temperature after : (a) 2 min. (b) 20 min.
arrow_forward
I need the answer as soon as possible
arrow_forward
8. The frequency of vibration can be used to monitor the change in mass. For example, the vibration frequency of a hospital bed can be used to monitor the patient's mass without moving the patient from the bed. One patient's mass was 54.4 kg, so the vibration frequency of the patient-bed system was 100.4 Hz. In the next measurement, the vibration frequency of the patient-bed system was 100 Hz.
arrow_forward
I am struggling with a, b,c,d
arrow_forward
SEE MORE QUESTIONS
Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Related Questions
- Each time your heart beats, your blood pres- sure first increases and then decreases as the heart rests between beats. The maximum and minimum blood pressures are called the systolic and diastolic pressures, respectively. Your blood pressure reading is written as systolic/diastolic. A reading of 120/80 is considered normal. A certain person's blood pressure is modeled by the function p(1) = 115 + 25 sin(16071) where p(t) is the pressure in mmHg (millimeters of mer- cury), at time t measured in minutes. Find the blood pressure reading. How does this compare to normal blood pressure?arrow_forwardMechanical EngineeringFluid Mechanicsarrow_forwardReferences: 1-J.L Meriam and L. G. Kr. 2012. C. Hibbeler, Engineering Mecha tice Hall 2004, and E. R. Johnston, 'Vector Mec. ENGINEERING MECHANICS STATICS Example 6\ The t-component of the force F is known to be 75 N. Determine the n component and the magnitude of F. 72 F. 10° 30°arrow_forward
- Q1 A and Barrow_forward1:19 P N{ l 100% I A docs.google.com A block of mass m = 2 kg is attached to a spring with spring constant k = 200 N/m, and is set to oscillate on a friction-less horizontal surface. At time t = 0 its position is xO = 0 and its velocity is vo = +5 m/s. If the displacement is a cosine function, x(t)=A cos(wt+p), then which answer is correct about the oscillation amplitude A and the phase constant,p,: A = 0.25 m, and p = - T/2 A = 0.5 m, p = 0 A = 0.5 m, and p = r/2 A = 0.5 m, p = -T/2 A = 0.25 m, and p = t/2 Other: A body oscillates with simple harmonic frictionless motion along the x-axis. Its displacement varies ith time according to x(t)=0.5 cos(Tt). The ues of the velocity (in m/s) and acceleration (in m/s^2) of the 8 IIarrow_forwardPlease solve this question in handwriting step by step. Again Please in handwriting.arrow_forward
- Q3/ In real life engineering application, it is required to design a spring in train, which one of the following materials in the table below should be choose, justify your answer ? used correct units? Poisson's Yield Strength Modulus of Elasticity 106 psi Material MPа psi GPa Ratio 30 0.30 120000 207 Steel alloy Brass alloy Aluminum alloy Titanium alloy 830 0.34 0.33 380 55000 97 14 275 40000 69 10 690 100000 107 15.5 0.34arrow_forwardA mechanic is trying to tighten a giant bolt using a wrench. Forces are applied at points A and B. d₁ 0₁ 160 N 570 N 15 degrees 15 degrees 40 degrees 0.35 m 0.19 m F₁ clockwise N-m Which direction is Mo rotating? counter-clockwise d2 A 0₂ Values for the figure are given in the following table. Note the figure may not be to scale. Variable Value F₁ 03 X F₂ 0₁ 0₂ 03 d₁ d₂ a. Using Varignon's Theorem, determine the magnitude of the moment about the origin, Mo. Round your final answers to 3 significant digits/figures. Mo= F2arrow_forwardPHYS X PHYS X 印 PHYS X PHYS X POTPHYS X PHYS X E PHYS X E PHYS top/semester2/physics%20for%20engineers/PHYS220_CH15_Lecture%20Notes_Problems%2015 19,15.29 S (D Page view A Read aloud V Draw Problem-15-19: page-475 A 0.500-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 10.0 cm. Calculate the maximum value of its (a) speed, and acceleration. (b) the speed and the acceleration when the object is 6.00 em from the equilibrium position, and (c) the time interval required for the object to move from.r50 to r5 8.O0 cm. Solution:arrow_forward
- Thermodynamics Topic: Ideal Gas or Perfect Gas Solve completely in handwritten with given, req’d & sol’n Thank you!arrow_forwardTHERMODYNAMICS TOPIC: FIRST LAW OF THERMO/THERMODYNAMIC SYSTEM PLEASE ANSWER COMPLETELY THE QUESTION IN HANDWRITING AND SUPPORT YOUR SOLUTION WITH DIAGRAMS. THANK YOUarrow_forwardSolve the problem quick & carefully On a sheet of paper with FBD , Don't copy which might be wrong.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY