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Rina8888 [55]
3 years ago
9

A 16 foot ladder is leaning against a wall. If the top of the ladder slides down the wall at a rate of 3 feet per second, how fa

st is the bottom of the ladder moving along the ground when the bottom of the ladder is 4 feet from the wall? Leave your answer in exact form, simplified as much as possible. Do not include units.
Physics
1 answer:
JulsSmile [24]3 years ago
7 0

Answer:

11.625

Explanation:

L = length of the ladder = 16 ft

v_{y} = rate at which top of ladder slides down = - 3 ft/s

v_{x} = rate at which bottom of ladder slides

y = distance of the top of ladder from the ground

x = distance of bottom of ladder from wall = 4 ft

Using Pythagorean theorem

L² = x² + y²

16² = 4² + y²

y = 15.5 ft

Also using Pythagorean theorem

L² = x² + y²

Taking derivative both side relative to "t"

0 = 2x\frac{\mathrm{d} x}{\mathrm{d} t} + 2y\frac{\mathrm{d} y}{\mathrm{d} t}

0 = x v_{x} + y v_{y}

0 = 4 v_{x} + (15.5) (- 3)

v_{x} = 11.625 ft/s

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A 132 cm wire carries a current of 2.2 A. The wire is formed into a circular coil and placed in a B Field of intensity 1 T. a) F
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Given Information:

Length of wire = 132 cm = 1.32 m

Magnetic field = B =  1 T

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Required Information:

(a) Torque = τ = ?

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Answer:

(a) Torque = 0.305 N.m

(b) Number of turns = 1

Explanation:

(a) The current carrying circular loop of wire will experience a torque given by

τ = NIABsin(θ)   eq. 1

Where N is the number of turns, I is the current in circular loop, A is the area of circular loop, B is the magnetic field and θ is angle between B and circular loop.

We know that area of circular loop is given by

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So the area becomes

A = π(L/2πN)²

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A = L²/4πN²

Substitute A into eq. 1

τ = NI(L²/4πN²)Bsin(θ)

τ = IL²Bsin(θ)/4πN

The maximum toque occurs when θ is 90°

τ = IL²Bsin(90)/4πN

τ = IL²B/4πN

torque will be maximum for N = 1

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τ = 0.305 N.m

(b) The required number of turns for maximum torque is

N = IL²B/4πτ

N = 2.2*1.32²*1)/4π*0.305

N = 1 turn

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