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3 years ago

If an object has zero resultant force on it, can it be moving? Can it be accelerating?

Physics

1 answer:

hichkok12 [17]3 years ago

5 0

It's moving, in a straight line and at a constant speed. It can't be accelerating.

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A 1-kilogram mass is attached to a spring whose constant is 21 N/m, and the entire system is then submerged in a liquid that imp

amm1812

Answer:

the required value is $x(t) = \frac{7}{4} e^{-3t}-\frac{3}{4} e^{-7t}$

Explanation:

Given that,

mass, m = 1kg

spring constant k = 21N/M

damping force = $-\beta\frac{dx}{dt} = \frac{-10dx}{dt}$

$\beta = 10$

By Newtons second law ,

The diffrential equation of motion with damping is given by

$m\frac{d^2x}{dt^2} = -kx-\beta\frac{dx}{dt}$

substitute the value of m =1kg, k = 21N/M, and $\beta = 10$

$1\frac{d^2x}{dt^2} = -21x=10\frac{dx}{dt}$

$\frac{d^2x}{dt^2} + 10\frac{dx}{dt} + 21x = 0$

suppose the equation of the form $x =e^m^t$ ,

and the auxilliary equation is given by

$m^2 + 10m + 21 = 0\\\\m^2 + 7m+3m+21=0\\\\m(m+7)+3(m+7)=0\\\\(m+7)(m+3)=0\\\\m=-7\\m=-3$

The general solution for the above differential equation is

$x(t) =C_1e^{-3t}+C_2e^{-7t}$

Derivate with respect to t

$x'(t)=-3C_1e^{-3t}-7C_2e^{-7t}$

(a)

since time is 0 then mass is one meter below

so x(0) = 1

Also it start from rest , that implies , velocity is 0 and time is 0

$x'(0) = 0$

substitute the initial condition

$C_1 +C_2 = 1$

$-3C_1-7C_2=0$

Solve the above equation to get C₁ and C₂

$C_1 =\frac{7}{4} and C_2 = -\frac{3}{4}$

substitute for C₁ and C₂ in general solution

$x(t) = \frac{7}{4} e^{-3t}-\frac{3}{4} e^{-7t}$

Thus the required value is $x(t) = \frac{7}{4} e^{-3t}-\frac{3}{4} e^{-7t}$

3 0

3 years ago

Read 2 more answers

HELP ASAP

amid [387]

Answer:

3200 has the fewest number of sig figs

Explanation:

sorry i was late

7 0

3 years ago

5.<br>why does the pointer rotate?

morpeh [17]

Answer: find the answer in the explanation.

Explanation:

From the experiment set up in the diagram, the pointer is resting on the drinking straw while the rod is resting on the drinking straw.

When the rod is being heated through the bursen burner, there will be linear expansion in the rod. As the rod increases its length, this causes the drinking straw to roll and thereby causing the pointer to rotate.

The pointer therefore rotates because of the thermer expansion that happen in the rod due to the heat from the bursen burner.

8 0

3 years ago

What results when energy is transformed while juggling three bowling pins?

Nady [450]

Answer:

his is an example of the transformation of gravitational potential energy into kinetic energy

Explanation:

The game of juggling bowling is a clear example of the conservation of mechanical energy,

when the bolus is in the upper part of the path mechanical energy is potential energy; As this energy descends, it becomes kinetic energy where the lowest part of the trajectory, just before touching the hand, is totally kinetic.

At the moment of touching the hand, a relationship is applied that reverses the value of the speed, that is, now it is ascending and the cycle repeats.

Therefore this is an example of the transformation of gravitational potential energy into kinetic energy

8 0

3 years ago

Help me help me help me

spin [16.1K]

I think d because they are both increasing

7 0

3 years ago

Read 2 more answers