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Assume the following values: d1 = 0.880 m , d2 = 1.11 m , d3 = 0.560 m , d4 = 2.08 m , F1 = 510 N , F2 = 306 N , F3 = 501 N , F4 = 407 N , and MA = 1504 N⋅m . Express the Cartesian components of the resultant force and the couple moment in newtons and newton-meters to three significant figures separated by commas.

Answers

Answer 1

Answer:

= 2630.6 N.m

Explanation:

(FR)x = ΣFx = -F4 = -407 N

(FR)y = ΣFy =-F1-F2 -F3 = -510 - 306 - 501 = -1317 N

(MR)B =ΣM + Σ(±Fd)

= MA + F1(d1 +d2) + F2d2 - F4d3

= 1504 + 510(0.880+1.11) +306(1.11) - 407(0.560)

= 2630.64 N.m (counterclockwise)

Answer 2

Answer:

Final answer:

The Cartesian components of the resultant force and the couple moment are calculated by summing up all the forces and moments acting on the object. The resultant force is 1724 N and the couple moment is 29.764 N*m.

Explanation:

The resultant force and couple moment in the Cartesian coordinate system can be obtained by summing up all the forces and moments acting on the object. In this case, we have the forces F1, F2, F3, F4 and the couple moment MA acting on the object. The resultant force (FR) can be calculated as the sum of all the forces, i.e., FR = F1 + F2 + F3 + F4. Using the values given, FR = 510 N + 306 N + 501 N + 407 N = 1724 N. The resultant moment (MR) can be calculated as the sum of all the moments, i.e., MR = d1*F1 + d2*F2 + d3*F3 + d4*F4 - MA. Using the values given, MR = 0.880 m * 510 N + 1.11 m * 306 N + 0.560 m * 501 N + 2.08 m * 407 N - 1504 N*m = 29.764 N*m. Therefore, the Cartesian components of the resultant force and the couple moment are 1724 N and 29.764 N*m respectively.

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Answers

Answer:

Work done W =1406.25 J

Explanation:

Work done on a body can be calculated using newton's 2nd laws:

F=ma

$\Rightarrow a=(F)/(m)$

Hence acceleration of the block is given by:

$\Rightarrow a=(25)/(2)=12.5m/s^2$

Displacement of the object is given by:

$\Rightarrow S=ut+(1)/(2)at^2$

Substitute the values

$\Rightarrow S=0*3+(1)/(2)(12.5)3^2$

$\Rightarrow S=56.25 m$

Now work done is given by:

W=F.S

W = 25×56.25

W =1406.25 J

The 9-inch-long elephant nose fish in the Congo River generates a weak electric field around its body using an organ in its tail. When small prey, or even potential mates, swim within a few feet of the fish, they perturb the electric field. The change in the field is picked up by electric sensor cells in the skin of the elephant nose. These remarkable fish can detect changes in the electric field as small as 3.00 μN/C. How much charge, modeled as a point charge, in the fish would be needed to produce such a change in the electric field at a distance of 63.5 cm ?

Answers

Answer:

$1.34\cdot 10^(-16) C$

Explanation:

The strength of the electric field produced by a charge Q is given by

$E=k(Q)/(r^2)$

where

Q is the charge

r is the distance from the charge

k is the Coulomb's constant

In this problem, the electric field that can be detected by the fish is

$E=3.00 \mu N/C = 3.00\cdot 10^(-6)N/C$

and the fish can detect the electric field at a distance of

$r=63.5 cm = 0.635 m$

Substituting these numbers into the equation and solving for Q, we find the amount of charge needed:

$Q=(Er^2)/(k)=((3.00\cdot 10^(-6) N/C)(0.635 m)^2)/(9\cdot 10^9 Nm^2 C^(-2))=1.34\cdot 10^(-16) C$

A conducting loop of radius r=0.1 m, carrying a current I=2 A has a magnetic moment \vec{\mu} μ that is entirely in the j-hat direction. The loop is immersed in a magnetic field \vec{B} B = [3 i-hat + 4 j-hat] T. What is the potential energy of the loop in this configuration?

Answers

Answer:

Explanation:

Magnetic moment of current carrying loop

= current x area

= 2 x π x .1²

M = .0628 unit . it is in j direction so vecor form of it

M = .0628 j

Magnetic field B = 3i + 4 j

Energy

= - M.B

- .0628 j . ( 3i + 4 j )

= - .2512 J

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Answers

Answer:

liquids

Explanation

Which if, any, of these statements are true? (More than one may be true.) Assume the batteries are ideal. Check all that apply. A battery supplies the energy to a circuit. A battery is a source of potential difference; the potential difference between the terminals of the battery is always the same. A battery is a source of current; the current leaving the battery is always the same.

Answers

Answer:

All are true except the last point that says that a battery is a current source and the current at the outlet is always the same.

Explanation:

A battery is an electro-chemical device which converts the chemical energy into usable electrical energy thus it provides electrical energy.
Since, the battery maintains a a constant potential difference between its terminals, once connected.
Since, the movement of electric current requires energy, which is supplied by the electric potential energy stored in the battery.
The current in the battery flows as per the Ohm's law and we can not say that the current leaving will always remain constant.
As the current is the flow of electric charge, and charges are not stored in batteries unlike capacitors, thus the current at the leaving end will depend on Ohm's law and will vary accordingly.

Write down the DE of motion of a particle moving under the influence of gravity and experiencing a resistive force. .