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Stanford Engr 14 homework solutions for first pset - winter 2015
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Part 1. Getting Out in the World
(1.1) Drawing artifacts (5 pts) Find an interesting artifact in your kitchen, garage, or dorm room that is operated by a force or moment.
Create a storyboard (cartoon-like description) of how the artifact works, including how the force or
moment operates it. Examples of artifacts include a hand mixer, a hole punch, a nail clipper, the machines
in the weight room, or a car jack.
1. Hand Mixer 2. Exert force at the
handle for gripping.
3. Impose moment along
the handle to mix batter
F
F
M
(1.2) Calibrating Your Capacity (5 pts) It is important for engineers to have a sense of how large forces are. One way of developing this sense is
to create reference frames for force comparison; one such reference is your physical capacity. To this
end, find a weight room on campus and record the following information, in the table format shown
below in Table 1. Rather than turning in the table, please input your results at the following link (this is
how you will be given credit for your work):
https://docs.google.com/forms/d/1pgcwHnMM3GGVzkNK_HM3YyFpQ_hWANM6nJ6VBpmOEnA/vie
wform
BENCH PRESS
Maximum weight without hurting yourself.
Weight you can do repetitively 20 times without hurting yourself.
LEG PRESS
Maximum weight without hurting yourself.
Weight you can do repetitively 20 times without hurting yourself.
ARM CURL
Maximum weight without hurting yourself.
Weight you can do repetitively 20 times without hurting yourself.
𝟏𝑵 = 𝟎. 𝟐𝟐𝟒𝟖𝒍𝒃
𝟏𝒍𝒃 = 𝟒. 𝟒𝟒𝟖𝟐𝑵
Students do not need to hand in a table. The following is just an example to show the data.
Part 2. A Foray into Analysis (5 pts)
(2.1) Read: ‘The Bicycle: “Static” doesn’t mean that you aren’t moving’
Goal: To provide a free-body diagram of the bicycle and cyclist traveling at constant speed, estimate the
maximum velocity on a bicycle if the coefficient of drag is reduced by 15% and provide two suggestions
on how to reduce aerodynamic drag.
Given: The values of the variables, which include 𝐴𝑓𝑟𝑜𝑛𝑡𝑎𝑙 = 0.5𝑚2, 𝐶𝑑 = 0.85 × 𝐶𝑑−𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 = 0.765
Assume: Since the question asks for maximum velocity, ‖𝑭𝑑𝑟𝑎𝑔‖ = 167𝑁. This is selected based on the
assumption that the cyclist sustains peak force throughout the stroke. Also, it is assumed that the cyclist is
cycling at sea level, which makes the air density 𝜌 = 1.2𝑘𝑔/𝑚3 for the problem.
Draw: Free-body diagram of the bicycle and the cyclist
Formulate Equations:
‖𝑭𝑑𝑟𝑎𝑔‖ = (𝐶𝑑𝜌𝐴
2) 𝑉2
𝑉𝑚𝑎𝑥 = √2 × ‖𝑭𝑑𝑟𝑎𝑔‖
𝐶𝑑𝜌𝐴
Solve:
𝑉𝑚𝑎𝑥 = √2 × 167𝑁
0.765 × 1.20𝑘𝑔/𝑚3 × 0.5𝑚2= 26.98𝑚/𝑠
Ways to Reduce Drag: The cyclist can wear a tighter clothes, an aerodynamic helmet, or use more
aerodynamic bike wheels.
𝑉𝑚𝑎𝑥 = 27.0𝑚/𝑠
(2.2) Read: ‘The Golden Gate Bridge’
Goal: To provide a free-body diagram of the bridge, estimate the minimum required anchorage weight if
the coefficient of friction is increased by 15% and two suggestions of how to increase the coefficient of
friction.
Given: Friction force that prevents sliding, ‖𝑭𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛,𝑎𝑛𝑐ℎ𝑜𝑟𝑎𝑔𝑒‖ = 236.5𝑀𝑁, vertical force from table,
‖𝑭𝐻𝑂,𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙‖ = 84.7𝑀𝑁, coefficient of friction, 𝜇𝑠𝑡𝑎𝑡𝑖𝑐 = 1.15 × 𝜇𝑠𝑡𝑎𝑡𝑖𝑐,𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 = 0.69
Assume: The system is planar.
Draw: Free-body diagram of the bridge and the anchorage
Formulate Equations:
‖𝑭𝑛𝑜𝑟𝑚𝑎𝑙,𝑎𝑛𝑐ℎ𝑜𝑟𝑎𝑔𝑒‖ =‖𝑭𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛,𝑚𝑎𝑥‖
𝜇𝑠𝑡𝑎𝑡𝑖𝑐
‖𝑾𝑎𝑛𝑐ℎ𝑜𝑟𝑎𝑔𝑒,𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑‖ = ‖𝑭𝑛𝑜𝑟𝑚𝑎𝑙,𝑎𝑛𝑐ℎ𝑜𝑟𝑎𝑔𝑒‖ + ‖𝑭𝐻𝑂 𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙‖
Solve:
‖𝑾𝑎𝑛𝑐ℎ𝑜𝑟𝑎𝑔𝑒,𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑‖ =236.5𝑀𝑁
0.69+ 84.7𝑀𝑁 = 427.45𝑀𝑁
Ways to Increase Friction: Rougher surface between the ground and the anchorage, using adhesives,
tighter bolts to achieve better surface mating between ground and anchorage.
‖𝑾𝑎𝑛𝑐ℎ𝑜𝑟𝑎𝑔𝑒,𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑‖ = 427𝑀𝑁
Part 3. Representing and Labeling Forces & Vectors
Make sure that your answers to the problems in this section include all calculations you performed and a
supporting drawing(s).
Furthermore, show only the number of significant figures appropriate for precision of given data: A
practical rule in engineering calculations is to use four figures to record numbers with a leading “1” and
three figures in all other cases in presenting your final answer. Intermediate calculation steps should retain
more significant figures. With this rule, a force of 40 is 40.0 N, and a force of 15 is 15.00 N. Numbers are
generally rounded (as opposed to truncated) in reporting values to the correct number of significant
figures. For example, 29.694 N would be written with three significant figures as 29.7 N with rounding
(and not as 29.6 N, which is what we would get if we truncated the answer).
(3.1) External, Internal and Not-in-System Forces (5 pts) A person grips a pair of locking jaw pliers (more commonly known as vise-grips), as shown in Figure 1,
in order to tighten a nut onto a bolt. Three cases (systems) are described in the top row of Table 2. For
each system identify the external (E), internal (I) and Not-in-System (NIS) forces, and indicate them in
Table 2, including a sketch of each system in the space provided. (It is ok to turn in the next page with
your homework.)
Figure 1
(3.1) continued. (Turn in this page with your homework)
Table 2
Forces
Case 1:
Nut is defined as
the system
Case 2:
Nut and vise-
grips defined as
the system
Case 3:
Vise-grips
defined as the
system
Case 4:
Member C
defined as the
system
Tension in spring NIS I I E
Normal contact
between pin A
and member B NIS I I E
Normal contact
between pin A
and member C NIS I I I
Normal contact
between nut and
member B E I E NIS
Normal contact
between nut and
member C E I E E
Normal contact
and friction
forces between
thumb and vise-
grips at D
NIS E E NIS
Normal and
friction forces
between fingers
and vise-grips at
E
NIS E E E
Weight of vise-
grips NIS E E E, Partially
Weight of nut E E NIS NIS
Normal contact
and friction
forces between
nut and bolt
E E NIS NIS
Sketches of the four systems:
Vice-grips and nut Vice-grips Nut Member C
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