Suppose you have 50 grams of isotope with a half life of 2 years. How much is the isotope will you have after 4 years

A tank of volume 0.25 ft is designed to contain 50 standard cubic feet of air. The temperature is 80° F.Calculate the pressure i

slavikrds [6]

Answer:

The inside Pressure of the tank is $4499.12 lb/ft^{2}$

Solution:

As per the question:

Volume of tank, $V = 0.25 ft^{3}$

The capacity of tank, $V' = 50ft^{3}$

Temperature, T' = $80^{\circ}F$ = 299.8 K

Temperature, T = $59^{\circ}F$ = 288.2 K

Now, from the eqn:

PV = nRT (1)

Volume of the gas in the container is constant.

V = V'

Similarly,

P'V' = n'RT' (2)

Also,

The amount of gas is double of the first case in the cylinder then:

n' = 2n

$\]frac{n'}{n} = 2$

where

n and n' are the no. of moles

Now, from eqn (1) and (2):

$\frac{PV}{P'V'} = \frac{nRT}{n'RT'}$

$P' = 2P\frac{T'}{T} = 2\times 2116\times \frac{299.8}{288.2} = 4499.12 lb/ft^{2}$

7 0

4 years ago

The displacement of a 500 g mass, undergoing simple harmonic motion, is defined by the function :

Delicious77 [7]

The maximum kinetic energy, maximum potential energy and the maximum mechanical energy are equal to 7.56J.

<h3>What is simple harmonic motion?</h3>

Simple harmonic motion, in physics, repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side.

Simple Harmonic Motion

The given equation of the simple harmonic motion is

$x=3.5 sin (\frac{\pi }{2t} + \frac{5\pi }{4} )$

Data;

ω = π/2

k = 1.254N/m

Solving this

$\frac{dx}{dt} = -3.5 X \frac{\pi }{2} cos (\frac{x\pi t}{2}+\frac{5\pi }{4} )$

Let's calculate the maximum velocity.

$V_{m} =\frac{3.5\pi }{2}$

This is only possible when cos θ = -1

The maximum kinetic energy is

$K_m =\frac{1}{2} mv^2 = \frac{1}{2} X \frac{500}{1000} X \frac{7^2\pi ^2}^{4} ^2$

$w^2 = \frac{k}{m} \\k = w^2m\\k = \frac{\pi ^2}{4} X \frac{500}{1000} \\k =1.254 N/m$

Using the value of spring constant, we can find the maximum potential energy.

$P.E =\frac{1}{2} k x^2\\P.E =\frac{1}{2} X 1.234 X 3.5^2 \\P.E = 7.56 J$

The maximum potential energy is 7.56J

The maximum mechanical energy is equal to the sum of maximum potential energy and the maximum kinetic energy.

ME = K.E + P.E

ME = 7.56J

From the calculations above, the maximum kinetic energy, maximum potential energy and the maximum mechanical energy are equal to 7.56J.

Learn more on simple harmonic motion here;

brainly.com/question/15556430

#SPJ1

8 0

2 years ago

A body travels at an initial speed of 2.5 m/s. Given a constant acceleration of 0.2 m/s 2 what is the speed of the body at time

garri49 [273]

Answer:

<u>We are given:</u>

u = 2.5 m/s

a = 0.2 m/s/s

t = 25 seconds

v = v m/s

<u>Solving for 'v':</u>

From the first equation of motion:

v = u + at

Replacing the values

v = 2.5 + (0.2)(25)

v = 2.5 + 5

v = 7.5 m/s

6 0

3 years ago

Car A, moving in a straight line at a constant speed of 20. meters per second, is initially 200 meters behind car B, moving in t

MA_775_DIABLO [31]

First, let's express the movement of Car A and B in terms of their position over time (relative to car B)
For car A: y=20x-200 Car A moves 20 meters every second x, and starts 200 meters behind car B
For Car B: y= 15x Car B moves 15 meters every second and starts at our basis point

Set the two equations equal to one another to find the time x at which they meet:
20x - 200 = 15x
200 = 5x
x= 40
At time x=40 seconds, the cars meet. How far will Car A have traveled at this time?
Car A moves 20 meters every second:
20 x 40 = 800 meters

8 0

3 years ago

Which change will increase the speed of a sound wave traveling in a solid aluminum rod? changing the rod from a solid to a liqui

Pepsi [2]

Answer:

increasing the temperature of the rod

Explanation:

Sound wave is a longitudinal wave and its speed in a solid rod is given by the formula

$v = \sqrt{\frac{Y}{\rho}}$

here we know that

Y = young's modulus

$\rho$ = density of the medium

so as we increase the temperature of rod the density of the rod will decrease while the elasticity will remain same

So on increasing the temperature we can say that speed will increase due to decrease in the density

4 0

3 years ago