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2 years ago

15

In our usual coordinate system( +x to the right, +y up (away from the center of the Earth), +z out of the page toward you), what

is the vector gravitational force on a 31 kg object sitting on the ground? (From the momentum principle you can conclude that a force of the same magnitude is exerted upward by the ground on the object if the momentum isn't changing. In Chapter 4 we'll see more about the origin of this force.)

1 answer:

skad [1K]2 years ago

5 0

Answer:

The vector gravitational force is $W = 303.8\ N( -y)$

Explanation:

From the question we are told that

The mass of the object is $m = 31 \ kg$

The acceleration due to gravity experienced by the object is $g = 9.8 m/s^2$

Generally the vector gravitational force on the object is mathematically represented as

$W = 31 * 9.8$

$W = 303.8\ N (-y)$

The -y indicates that the direction of the force is towards the center of the earth

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A 100-W (watt) light bulb has resistance R=143Ω (ohms) when attached to household current, where voltage varies as V=V0sin(2πft)

Phantasy [73]

Complete Question

A 100-W (watt) light bulb has resistance R=143Ω (ohms) when attached to household current, where voltage varies as V=V0sin(2πft), where V0=110 V, f=60 Hz. The power supplied to the bulb is P=V2R J/s (joules per second) and the total energy expended over a time period [0,T] (in seconds) is $U = \int\limits^T_0 {P(t)} \, dt$

Compute U if the bulb remains on for 5h

Answer:

The value is $U = 7.563 *10^{5} \ J$

Explanation:

From the question we are told that

The power rating of the bulb is $P = 100 \ W$

The resistance is $R = 143 \ \Omega$

The voltage is $V = V_o sin [2 \pi ft]$

The energy expanded is $U = \int\limits^T_0 {P(t)} \, dt$

The voltage $V_o = 110 \ V$

The frequency is $f = 60 \ Hz$

The time considered is $t = 5 \ h = 18000 \ s$

Generally power is mathematically represented as

$P = \frac{V^2}{ R}$

=> $P = \frac{( 110 sin [2 \pi * 60t])^2}{ 144}$

=> $P = \frac{ 110^2 [ sin [120 \pi t])^2}{ 144}$

So

$U = \int\limits^T_0 { \frac{ 110^2* [sin [120 \pi t])^2}{ 144}} \, dt$

=> $U = \frac{110^2}{144} \int\limits^T_0 { ( sin^2 [120 \pi t]} \, dt$

=> $U = \frac{110^2}{144} \int\limits^T_0 { \frac{1 - cos 2 (120\pi t)}{2} } \, dt$

=> $U = \frac{110^2}{144} \int\limits^T_0 { \frac{1 - cos 240 \pi t)}{2} } \, dt$

=> $U = \frac{110^2}{144} [\frac{t}{2} - [\frac{1}{2} * \frac{sin(240 \pi t)}{240 \pi} ] ]\left | T} \atop {0}} \right.$

=> $U = \frac{110^2}{144} [\frac{t}{2} - [\frac{1}{2} * \frac{sin(240 \pi t)}{240 \pi} ] ]\left | 18000} \atop {0}} \right.$

$U = \frac{110^2}{144} [\frac{18000}{2} - [\frac{1}{2} * \frac{sin(240 \pi (18000))}{240 \pi} ] ]$

=> $U = 7.563 *10^{5} \ J$

7 0

3 years ago

(b) Un bloque rectangular de madera se mide con dimensiones de 11.2 cm x 3.4 cm x

vlabodo [156]

Answer:

V = 156.13 [cm³]

Explanation:

El volumen de un solido con forma de paralepipedo se puede calcular por medio de la siguiente formula:

$V = ancho*largo*alto$

donde:

V = volumen [cm³]

ancho = 3.4 [cm]

largo = 11.2 [cm]

alto = 4.1 [cm]

Ahora reemplazando.

$V = 3.4*11.2*4.1\\V = 156.13 [cm^{3}]$

5 0

2 years ago

A man pushes on piano with mass 170 kg; it slides at constant velocity down a ramp that is inclined at 20.0 ∘ above the horizont

nikdorinn [45]

Answer

given,

mass of the piano = 170 kg

angle of the inclination = 20°

moves with constant velocity hence acceleration = 0 m/s²

neglecting friction

so, force required to pull the piano

F = m g sin θ

F = 170 × 9.81 × sin 20°

F = 570.39 N

so, force required by the man to push the piano is F = 570.39 N

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Which variety of moth, C or Y, is more likely to be killed by insect eating birds?

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Moth X is more likely to be eaten by insect killing birds first. This is because Moth Y blends in with the tree trunk more and is hidden from birds. Its wings camouflage with the tree trunk, hiding it from sight.

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