Period, frequency, Amplitude, wave speed and wave length

A 15,000 kg rocket traveling at +230 m/s turns on its engines. Over a 6.0 s period it burns 1,000 kg of fuel. An observer on the

lesya692 [45]

Answer:

a) $v = 312.791\,\frac{m}{s}$ , b) $a = 13.333\,\frac{m}{s^{2}}$

Explanation:

The problem is asking the rocket velocity and acceleration at t = 6 s.

a) The general equation of the rocket is:

$v=v_{o} -v_{ex}\cdot \ln \frac{m}{m_{o}}$

$v = 230\,\frac{m}{s}-(1200\,\frac{m}{s} )\cdot \ln \frac{14000\,kg}{15000\,kg}$

$v = 312.791\,\frac{m}{s}$

b) The acceleration experimented by the rocket is:

$a = \frac{v_{ex}}{m_{o}}\cdot \frac{dm}{dt}$

$a = \frac{1200\,\frac{m}{s} }{15000\,kg}\cdot \frac{1000\,kg}{6\,s}$

$a = 13.333\,\frac{m}{s^{2}}$

3 0

4 years ago

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A ski gondola is connected to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to th

xz_007 [3.2K]

Answer:

(a) 89 m/s

(b) 11000 N

Explanation:

Note that answers are given to 2 significant figures which is what we have in the values in the question.

(a) Speed is given by the ratio of distance to time. In the question, the time given was the time it took the pulse to travel the length of the cable twice. Thus, the distance travelled is twice the length of the cable.

$v=\dfrac{2\times 620 \text{ m}}{14\text{ s}} = \dfrac{1240\text{ m}}{14\text{ s}}=88.571428\ldots \text{ m/s}= 89\text{ m/s}$

(b) The tension, $T$ , is given by

$v =\sqrt{\dfrac{T}{\mu}}$

where $v$ is the speed, $T$ is the tension and $\mu$ is the mass per unit length.

Hence,

$T = \mu\cdot v^{2}$

To determine $\mu$ , we need to know the mass of the cable. We use the density formula:

$\rho = \dfrac{m}{V}$

where $m$ is the mass and $V$ is the volume.

$m=\rho\cdot V$

If the length is denoted by $l$ , then

$\mu = \dfrac{m}{l} = \dfrac{\rho\cdot V}{l}$

$T = \dfrac{\rho\cdot V}{l} v^{2}$

The density of steel = 8050 kg/m3

The cable is approximately a cylinder with diameter 1.5 cm and length or height of 620 m. Its volume is

$V = \pi \dfrac{d^{2}}{4} l$

$T = \dfrac{\rho\cdot\pi d^2 l}{4l}v^2 = \dfrac{\rho\cdot\pi d^2}{4}v^2$

$T = \dfrac{8050\times\pi\times0.015^2}{4} \times 88.57^2$

$T = 11159.4186\ldots \text{ N} = 11000 \text{ N}$

4 0

4 years ago

The combination of all forces that act on an object are (2 points)

qaws [65]

Answer:

A) The net force

Explanation:

If two forces of equal strength act on an object in opposite directions, the forces will cancel, resulting in a net force of zero and no movement.

5 0

4 years ago

a0.155 kg arrow is shot from ground level, upward at 31.4 m/s. what is its kinetic energy (ke) when it is 30.0 m above the groun

swat32

The kinetic energy (KE) of a 0.155 kg arrow that is shot from ground level, upward at 31.4 m/s, when it is 30.0 m above the ground is 30.85 J

Assuming air friction is negligible,

a = - 9.8 m / s²

u = 31.4 m / s

s = 30 m

v² = u² + 2 a s

v² = 31.4² + ( 2 * - 9.8 * 30 )

v² = 985.96 - 588

v² = 397.96 m / s

KE = 1 / 2 m v²

KE = 1 / 2 * 0.155 * 397.96

KE = 0.0775 * 397.96

KE = 30.85 J

Therefore, the kinetic energy ( KE ) when it is 30.0 m above the ground is 30.85 J

To know more about kinetic energy

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5 0

2 years ago

Does passing a magnet through a coil of wire break off it’s electric current

hichkok12 [17]

A magnetic field is actually generated by a moving current (or moving electric charge specifically). The magnetic field generated by a moving current can be found by using the right hand rule, point your right thumb in the direction of current flow, then the wrap of your fingers will tell you what direction the magnetic field is. In the case of current traveling up a wire, the magnetic field generated will encircle the wire. Similarly electromagnets work by having a wire coil, and causing current to spin in a circle, generating a magnetic field perpendicular to the current flow (again right hand rule).

So if you were to take a permenant magnet and cut a hole in it then string a straight wire through it... my guess is nothing too interesting would happen. The two different magnetic fields might ineteract in a peculiar way, but nothing too fascinating, perhaps if you give me more context as to what you might think would happen or what made you come up with this question I could help.

Source: Bachelor's degree in Physics.

7 0

3 years ago