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A pendulum consists of a large balanced mass hanging on the end of a long wire. At the point where a 28-kg pendulum has the grea

Ray Of Light [21]

Answer:

The length of the wire is approximately 67.1 m

Explanation:

The parameters of the pendulum are;

The mass of the pendulum, m = 28 kg

The angle between the pendulum weight and the wire, θ = 89°

The magnitude of the torque exerted by the pendulum's weight, τ = 1.84 × 10⁴ N·m

We have;

Torque, τ = F·L·sinθ = m·g·l·sinθ

Where;

F = The applies force = The weight of the pendulum = m·g

g = The acceleration due to gravity ≈ 9.8 m/s²

l = The length of the wire

Plugging in the values of the variables gives;

1.84 × 10⁴ N·m = 28 kg × 9.8 m/s² × l × sin(89°)

Therefore;

l = 1.84 × 10⁴ N·m/(28 kg × 9.8 m/s² × sin(89°)) = 67.0656080029 m ≈ 67.1 m

The length of the wire, l ≈ 67.1 m

6 0

3 years ago

Ohm's law states which relationship between electrical quantities? a. Volts = current x resistance b. Volts = current divided by

miv72 [106K]

Answer:

a. Volts = current x resistance

Explanation:

Ohm's law states that at constant temperature, the current flowing in an electrical circuit is directly proportional to the voltage applied across the two points and inversely proportional to the resistance in the electrical circuit.

Mathematically, Ohm's law is given by the formula;

$V = IR$

Where;

V represents voltage measured in voltage.

I represents current measured in amperes.

R represents resistance measured in ohms.

Hence, Ohm's law gives the relationship between voltage, current and resistance of an electric circuit.

7 0

2 years ago

Three short square wood blocks measuring 3.5 per side support a machine weighing 29500 lbs. What is the compressive stress in th

Ilya [14]

Answer:

D. 803 lbs

Explanation:

In order to find the compressive stress on all three blocks we first need to find the normal surface area of each:

Surface Area of 1 Block = 3.5 x 3.5

Surface Area of 1 Block = 12.25

Surface Area of all 3 Blocks = A = 3 x 12.25

Area = 36.75

Now, the stress is given by the following formula:

Stress = Force/Area

Stress = 29500 lbs/36.75

Stress = 802.72 lbs

Hence, the correct option will be:

4 0

3 years ago

A projectile of mass m is fired horizontally with an initial speed of v0 from a height of h above a flat, desert surface. Negle

Grace [21]

Complete question is;

A projectile of mass m is fired horizontally with an initial speed of v0 from a height of h above a flat, desert surface. Neglecting air friction, at the instant before the projectile hits the ground, find the following in terms of m, v0, h and g:

(a) the work done by the force of gravity on the projectile,

(b) the change in kinetic energy of the projectile since it was fired, and

(c) the final kinetic energy of the projectile.

(d) Are any of the answers changed if the initial angle is changed?

Answer:

A) W = mgh

B) ΔKE = mgh

C) K2 = mgh + ½mv_o²

D) No they wouldn't change

Explanation:

We are expressing in terms of m, v0, h, and g. They are;

m is mass

v0 is initial velocity

h is height of projectile fired

g is acceleration due to gravity

A) Now, the formula for workdone by force of gravity on projectile is;

W = F × h

Now, Force(F) can be expressed as mg since it is force of gravity.

Thus; W = mgh

Now, there is no mention of any angles of being fired because we are just told it was fired horizontally.

Therefore, even if the angle is changed, workdone will not change because the equation doesn't depend on the angle.

B) Change in kinetic energy is simply;

ΔKE = K2 - K1

Where K2 is final kinetic energy and K1 is initial kinetic energy.

However, from conservation of energy, we now that change in kinetic energy = change in potential energy.

Thus;

ΔKE = ΔPE

ΔPE = U2 - U1

U2 is final potential energy = mgh

U1 is initial potential energy = mg(0) = 0. 0 was used as h because at initial point no height had been covered.

Thus;

ΔKE = ΔPE = mgh

Again like a above, the change in kinetic energy will not change because the equation doesn't depend on the angle.

C) As seen in B above,

ΔKE = ΔPE

Thus;

½mv² - ½mv_o² = mgh

Where final kinetic energy, K2 = ½mv²

And initial kinetic energy = ½mv_o²

Thus;

K2 = mgh + ½mv_o²

Similar to a and B above, this will not change even if initial angle is changed

D) All of the answers wouldn't change because their equations don't depend on the angle.

5 0

3 years ago

Consider three resistors with unequal resistances connected in series to a battery. Which of the following statements are true?

Ivenika [448]

<h2>Answer: The second Statement </h2>

<h2>The algebraic sum of the currents flowing through each of the three resistors is equal to the current through the battery. </h2><h2 />

In a series circuit, the value of the equivalent resistance $R_E$ is equal to the sum of the values of each of them:

$R_ {E}=R_{1}+R_ {2}+R_ {3}$

Where:

<h2>The equivalent resistance of the combination of resistors is greater than the resistance of any one of three resistors. </h2>

In this case the current $I$ flowing through the resistors is the same in each one. This is because the current flowing through the circuit only has one way to go, so the current intensity is the same throughout the circuit.

Therefore:

<h2>The current flowing through each of the resistors is the same and is equal to the current through the battery. </h2><h2>The algebraic sum of the voltages across the three resistors is equal to the voltage across the battery. </h2>

The battery provides a voltage $V_T$ that is the sum of the different voltages at the ends of the resistors:

$V_{T}=V_{1}+V_{2}+V_{3}$

Where the Voltage, according to Ohm's law is:

$V=R.I$

Hence, the second statement of this question is <u>True </u>

7 0

3 years ago