<< Chapter < Page Chapter >> Page >

The bathroom scale is an excellent example of a normal force acting on a body. It provides a quantitative reading of how much it must push upward to support the weight of an object. But can you predict what you would see on the dial of a bathroom scale if you stood on it during an elevator ride? Will you see a value greater than your weight when the elevator starts up? What about when the elevator moves upward at a constant speed: will the scale still read more than your weight at rest? Consider the following example.

What does the bathroom scale read in an elevator?

[link] shows a 75.0-kg man (weight of about 165 lb) standing on a bathroom scale in an elevator. Calculate the scale reading: (a) if the elevator accelerates upward at a rate of 1 . 20 m/s 2 size 12{1 "." "20 m/s" rSup { size 8{2} } } {} , and (b) if the elevator moves upward at a constant speed of 1 m/s.

A person is standing on a bathroom scale in an elevator. His weight w is shown by an arrow pointing downward. F sub s is the force of the scale on the person, shown by a vector starting from his feet pointing vertically upward. W sub s is the weight of the scale pointing vertically downward. W sub e is the weight of the elevator, shown by the broken arrow pointing vertically downward. F sub p is the force of the person on the scale, acting vertically downward. F sub t is the force of the scale on the floor of the elevator, pointing vertically downward, and N is the normal force of the floor on the scale, pointing upward. (b) The same person is shown on the scale in the elevator, but only a few forces are shown acting on the person, which is our system of interest. W is shown by an arrow acting downward, and F sub s is the force of the scale on the person, shown by a vector starting from his feet pointing vertically upward. The free-body diagram is also shown, with two forces acting on a point. F sub s acts vertically upward, and w acts vertically downward.
(a) The various forces acting when a person stands on a bathroom scale in an elevator. The arrows are approximately correct for when the elevator is accelerating upward—broken arrows represent forces too large to be drawn to scale. T size 12{T} is the tension in the supporting cable, w size 12{w} is the weight of the person, w s size 12{w rSub { size 8{s} } } {} is the weight of the scale, w e size 12{w rSub { size 8{e} } } {} is the weight of the elevator, F s size 12{F rSub { size 8{s} } } {} is the force of the scale on the person, F p size 12{F rSub { size 8{p} } } {} is the force of the person on the scale, F t size 12{F rSub { size 8{t} } } {} is the force of the scale on the floor of the elevator, and N size 12{N} is the force of the floor upward on the scale. (b) The free-body diagram shows only the external forces acting on the designated system of interest—the person.

Strategy

If the scale is accurate, its reading will equal F p size 12{F rSub { size 8{p} } } {} , the magnitude of the force the person exerts downward on it. [link] (a) shows the numerous forces acting on the elevator, scale, and person. It makes this one-dimensional problem look much more formidable than if the person is chosen to be the system of interest and a free-body diagram is drawn as in [link] (b). Analysis of the free-body diagram using Newton’s laws can produce answers to both parts (a) and (b) of this example, as well as some other questions that might arise. The only forces acting on the person are his weight w size 12{w} {} and the upward force of the scale F s size 12{F rSub { size 8{s} } } {} . According to Newton’s third law F p size 12{F rSub { size 8{p} } } {} and F s size 12{F rSub { size 8{s} } } {} are equal in magnitude and opposite in direction, so that we need to find F s size 12{F rSub { size 8{s} } } {} in order to find what the scale reads. We can do this, as usual, by applying Newton’s second law,

F net = ma size 12{F rSub { size 8{"net"} } = ital "ma"} {} .

From the free-body diagram we see that F net = F s w size 12{F rSub { size 8{"net"} } =F rSub { size 8{s} } - w} {} , so that

F s w = ma size 12{F rSub { size 8{s} } - w= ital "ma"} {} .

Solving for F s size 12{F rSub { size 8{s} } } {} gives an equation with only one unknown:

F s = ma + w size 12{F rSub { size 8{s} } = ital "ma"+w} {} ,

or, because w = mg , simply

F s = ma + mg size 12{F rSub { size 8{s} } = ital "ma"+ ital "mg"} {} .

No assumptions were made about the acceleration, and so this solution should be valid for a variety of accelerations in addition to the ones in this exercise.

Solution for (a)

In this part of the problem, a = 1.20 m/s 2 size 12{a=1 "." "20"" m/s" rSup { size 8{2} } } {} , so that

F s = ( 75 . 0 kg ) ( 1 . 20 m/s 2 ) + ( 75 . 0 kg ) ( 9 . 80 m/s 2 ) size 12{F rSub { size 8{s} } = \( "75" "." "0 kg" \) \( 1 "." "20 m/s" rSup { size 8{2} } \) + \( "75" "." "0 kg" \) \( 9 "." "80 m/s" rSup { size 8{2} } \) } {} ,

yielding

F s = 8 25 N size 12{F rSub { size 8{s} } =8"25 N"} {} .

Discussion for (a)

This is about 185 lb. What would the scale have read if he were stationary? Since his acceleration would be zero, the force of the scale would be equal to his weight:

F net = ma = 0 = F s w F s = w = mg F s = ( 75.0 kg ) ( 9. 80 m/s 2 ) F s = 735 N. alignl { stack { size 12{F rSub { size 8{"net"} } = ital "ma"=0=F rSub { size 8{s} } - w} {} #F rSub { size 8{s} } =w= ital "mg" {} # F rSub { size 8{s} } = \( "75" "." 0" kg" \) \( 9 "." "80 m/s" rSup { size 8{2} } \) {} #F rSub { size 8{s} } ="735"" N" "." {} } } {}

Questions & Answers

what is specific heat capacity of watee
paul Reply
I am so dull in physics please I need help
Sharon Reply
i am Physics professor its my Whats app contct no 9203366398003
ghulam
i am Physics professor
ghulam
923366398003
ghulam
923366398003 my whats apl no
ghulam
Thank God
Sharon
How do we begin sir
Sharon
where are from you
ghulam
i need help
Khamis
yes
ghulam
yes asked question
ghulam
Khamis Khan where are from you
ghulam
Am a Ghanaian
Sharon
But am in Nigeria
Sharon
Can I drop my number for lectures
Sharon
I am in Nigeria, Surulere, Lagos to be precise. I am a physics teacher and can help you. join my google class or whatsapp class@ +2348174872896
fitzgerald
abrahampaye8864@gmail.com
abraham
add me on whatsapp +2348141106356
lasisi
Me too
yusuf
Nigeria too
yusuf
ok
paul
In Inelastic collision cunculate the vilocity
Anshu Reply
elucidate
Usman
yes, find velocity (v) because the mass of two objects is decreased when stuck together. if the mass in the system increases than the velocity decreases respectively
Shii
explain how a body becomes electrically charged based on the presence of charged particles
Kym Reply
induction
babar
induction
DEMGUE
definitely by induction
Raymond
induction
Raymond
induction
Shah
induction
Korodhso
please why does a needle sinks in water
DEMGUE
induction
Korodhso
induction
Auwal
what are the calculations of Newton's third law of motiow
Murtala Reply
what is dark matter
apex Reply
(in some cosmological theories) non-luminous material which is postulated to exist in space and which could take either of two forms: weakly interacting particles ( cold dark matter ) or high-energy randomly moving particles created soon after the Big Bang ( hot dark matter ).
Usman
if the mass of a trolley is 0.1kg. calculate the weight of plasticine that is needed to compensate friction. (take g=10m/s and u=0.2)
Declan Reply
what is a galaxy
Maduka Reply
a galaxy is a type of phone e.g samsung galaxy there are diff types of samsung galaxy there is s5 s6 s7 s8 s9
lasisi
what isflow rate of volume
Abcd Reply
flow rate is the volume of fluid which passes per unit time;
Rev
flow rate or discharge represnts the flow passing in unit volume per unit time
bhat
When two charges q1 and q2 are 6 and 5 coulomb what is ratio of force
Mian Reply
incomplete question
lasisi
When reducing the mass of a racing bike, the greatest benefit is realized from reducing the mass of the tires and wheel rims. Why does this allow a racer to achieve greater accelerations than would an identical reduction in the mass of the bicycle’s frame?
bimo Reply
is that the answer
nehemiah
why is it proportional
nehemiah Reply
i don't know
Adah
y
nehemiah
what are the relationship between distance and displacement
Usman Reply
They are interchangeable.
Shii
Distance is scalar, displacement is vector because it must involve a direction as well as a magnitude. distance is the measurement of where you are and where you were displacement is a measurement of the change in position
Shii
Thanks a lot
Usman
I'm beginner in physics so I can't reason why v=u+at change to v2=u2+2as and vice versa
Usman
what is kinematics
praveen
kinematics is study of motion without considering the causes of the motion
Theo
The study of motion without considering the cause 0f it
Usman
why electrons close to the nucleus have less energy and why do electrons far from the nucleus have more energy
Theo
thank you frds
praveen
plz what is the third law of thermodynamics
Chidera Reply
third law of thermodynamics states that at 0k the particles will collalse its also known as death of universe it was framed at that time when it waa nt posible to reach 0k but it was proved wrong
bhat
I have not try that experiment but I think it will magnet....
Rev Reply
Hey Rev. it will
Jeff
I do think so, it will
Chidera
yes it will
lasisi

Get the best College physics course in your pocket!





Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask