1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lawyer [7]
3 years ago
15

A man is standing on a weighing machine on a ship which is bobbing up and down with simple harmonic motion of period T=15.0s.Ass

uming the motion is vertical calculate the amplitude of the ship's motion, if the scale reading of the machine varies between limits of 55.0kg and 65.0kg.
Physics
1 answer:
STALIN [3.7K]3 years ago
8 0

Well, first of all, one who is sufficiently educated to deal with solving
this exercise is also sufficiently well informed to know that a weighing
machine, or "scale", should not be calibrated in units of "kg" ... a unit
of mass, not force.  We know that the man's mass doesn't change,
and the spectre of a readout in kg that is oscillating is totally bogus.

If the mass of the man standing on the weighing machine is 60kg, then
on level, dry land on Earth, or on the deck of a ship in calm seas on Earth,
the weighing machine will display his weight as  588 newtons  or as 
132.3 pounds.  That's also the reading as the deck of the ship executes
simple harmonic motion, at the points where the vertical acceleration is zero.

If the deck of the ship is bobbing vertically in simple harmonic motion with
amplitude of M and period of 15 sec, then its vertical position is 

                                     y(t) = y₀ + M sin(2π t/15) .

The vertical speed of the deck is     y'(t) = M (2π/15) cos(2π t/15)

and its vertical acceleration is          y''(t) = - (2πM/15) (2π/15) sin(2π t/15)

                                                                = - (4 π² M / 15²)  sin(2π t/15)

                                                                = - 0.1755 M sin(2π t/15) .

There's the important number ... the  0.1755 M.
That's the peak acceleration.
From here, the problem is a piece-o-cake.

The net vertical force on the intrepid sailor ... the guy standing on the
bathroom scale out on the deck of the ship that's "bobbing" on the
high seas ... is (the force of gravity) + (the force causing him to 'bob'
harmonically with peak acceleration of  0.1755 x amplitude).

At the instant of peak acceleration, the weighing machine thinks that
the load upon it is a mass of  65kg, when in reality it's only  60kg.
The weight of 60kg = 588 newtons.
The weight of 65kg = 637 newtons.
The scale has to push on him with an extra (637 - 588) = 49 newtons
in order to accelerate him faster than gravity.

Now I'm going to wave my hands in the air a bit:

Apparent weight = (apparent mass) x (real acceleration of gravity)

(Apparent mass) = (65/60) = 1.08333 x real mass.

Apparent 'gravity' = 1.08333 x real acceleration of gravity.

The increase ... the 0.08333 ... is the 'extra' acceleration that's due to
the bobbing of the deck.

                        0.08333 G  =  0.1755 M

The 'M' is what we need to find.

Divide each side by  0.1755 :          M = (0.08333 / 0.1755) G

'G' = 9.0 m/s²
                                       M = (0.08333 / 0.1755) (9.8) =  4.65 meters .

That result fills me with an overwhelming sense of no-confidence.
But I'm in my office, supposedly working, so I must leave it to others
to analyze my work and point out its many flaws.
In any case, my conscience is clear ... I do feel that I've put in a good
5-points-worth of work on this problem, even if the answer is wrong .

You might be interested in
Experts, ACE, Genius... can anybody calculate for the Reactions at supports A and B please? Will give brainliest! Given: fb = 30
dybincka [34]

Answer:

Support at Cy = 1.3 x 10³ k-N

Support at Ay = 200 k-N

Explanation:

given:

fb = 300 k-N/m

fc = 100 k-N/m

D = 300 k-N

L ab = 6 m

L bc = 6 m

L cd = 6 m

To get the reaction A or C.

take summation of moment either A or C.

<em><u>Support Cy:</u></em>

∑ M at Ay = 0

      (( x1 * F ) + ( D * Lab ) + ( D * L bc + D * L cd )

Cy = -------------------------------------------------------------------

                                      ( L ab + L bc )

Cy = 1.3 x 10³ k-N

<em><u>Support Ay:</u></em>

Since ∑ F = 0,           A + C - F - D = 0

                                   A = F  + D - C

                                  Ay = 200 k-N

4 0
3 years ago
1. Calculate the average velocity of the following trip. You walk to Pershing Square 58
Gre4nikov [31]

Explanation:

Velocity = displacement / time

v = √((58 m)² + (135 m)²) / (12 min × 60 s/min)

v = 0.20 m/s

7 0
3 years ago
What is dark energy?
olga2289 [7]

Explanation:

Dark Energy. Dark Energy is a hypothetical form of energy that exerts a negative, repulsive pressure, behaving like the opposite of gravity. It has been hypothesised to account for the observational properties of distant type Ia supernovae, which show the universe going through an accelerated period of expansion

6 0
3 years ago
What is a glacier that terminates in the sea
alekssr [168]
Wound it be one that dissolves ?
5 0
3 years ago
A truck is carrying a steel beam of length 13.0 m on a freeway. An accident causes the beam to be dumped off the truck and slide
PIT_PIT [208]

Answer:

emf= 9.88 \times 10^{-3} T

Explanation:

Given:

  • Length of the beam, l=13\,m
  • speed of the beam, v=20\,m.s^{-1}
  • magnitude of the vertical magnetic field, B=38\times 10^{-6} T

According to the Faraday's law the emf induced in a rod passing transversely through a magnetic field is given as:

emf= l.v.B

emf=13\times 20\times 38\times 10^{-6}

emf= 9.88 \times 10^{-3} T

4 0
3 years ago
Other questions:
  • Raphael refers to a wave by noting its wavelength. lucinda refers to a wave by noting its frequency. which student is correct an
    15·1 answer
  • Soil formation involves both
    12·1 answer
  • Discuss the difference between waveform graphs and vibration graphs​
    15·1 answer
  • What is the kinetic energy of a 16g billiard ball moving at 2.5 m/s?​
    11·1 answer
  • A raised plaster cover (often called a plaster ring or mud ring) is permitted to increase the maximum number of conductors permi
    13·1 answer
  • Why must you use temperature to specify how hot or cold something is?
    13·2 answers
  • (25 Brainly Points.)
    14·1 answer
  • .
    5·1 answer
  • during a journey, a car travels at 40 km in 2.5 hours, next 62 km in 3 hours, then took a break for 30 minutes, again travelled
    9·1 answer
  • Ramu,the gardener,is trying to pull out weeds. however,he has to apply great force.why do you think he has to apply to much forc
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!