As a mass on a spring moves farther from the equilibrium position, how do the velocity, acceleration, and force

Two geological field teams are working in a remote area. A global positioning system (GPS) tracker at their base camp shows the

Masja [62]

Answer:

distance of 2nd team from 1st team will be: 58.2

Direction of 2nd team from 1st team will be: 14.90 deg North of east

Explanation:

ASSUME Vector is R and makes angle A with +x-axis,

therefore component of vector R is

$R_x = Rcos A$

$R_y = Rsin A$

From above relation

Assuming base camp as the origin, location of 1st team is

$R_1 = 37 km$ away at 21 deg North of west (North of west is in 2nd quadrant, So x is -ve and y is positive)

$R_{1x} = -R_1*cos A_1 = -37*cos 21 deg = -34.54 km$

$R_{1y} = R_1*sin A_1 = 37*sin 21 deg = 13.25 km$

location of 2nd team is at

$R_2 = 32 km$ , at 38 deg East of North = 32 km, at 58 deg North of east (North of east is in 1st quadrant, So x and y both are +ve)

$R_{2x} = R_2*cos A_2 = 32*cos 58 deg = 16.95 km$

$R_{2y} = R_2*sin A_2 = 32*sin 58 deg = 27.13 km$

Now position of 2nd team with respect to 1st team will be given by:

$R_3 = R_2 - R_1$

$R_3 = (R_{2x} - R_{1x}) i + (R_{2y} - R_{1y}) j$

Using above values:

$R_3 = (16.95 - (-34.54)) i + (27.13 - 13.42) j$

$R_3 = 51.49 i + 13.71 j$

distance of 2nd team from 1st team will be:

$\left | R_3 \right | = \sqrt (51.49^2 +13.71^2)$

$\left | R_3 \right | = 53.28 km = 58.2 km$

Direction of 2nd team from 1st team will be:

$Direction = tan^{-1} \frac{R_{3y}}{R_{3x}} = tan^{-1}[ \frac{13.71}{51.49}]$

Direction = 14.90 deg North of east

6 0

3 years ago

In your own words, explain why we see a rainbow or colorful sunset. Explain the properties and interactions that make this displ

Maksim231197 [3]

Wee see rainbows due to the geometries of the raindrops. when the sun shines behind, rays of light enter the raindrops and this light are refracted. The lights are then reflected from the back of the raindrop and refracted again as it passes the rain drop. Refraction in this sense is the cause for splitting the light into several colors.

7 0

4 years ago

A 5 kilograms bowling ball is dropped out a window. It hits the ground, and bounces upward. The velocity change of the ball is n

ioda

Answer:

13.5

Explanation:

Mass: 5kg

Initial Velocity: -15

Final Velocity: 12

Force: 10

We can use the equation: Vf = Vi + at

We need to find acceleration, and we can use the equation, F=ma,

We have mass and the force so it would look like this, 10=5a, and 5 times 2 would equal 10, so acceleration would be 2.

Now we have all the variables to find time.

Back to Vf = Vi + at, plug the numbers in, 12 = -15 + 2(t)

Plugging them in into desmos gives 13.5 for time.

4 0

2 years ago

A running back holds 0.25 kg football and runs 100m down the football field. In addition to scoring six points for his team, he

katrin2010 [14]

Answer:

<h2>1) there is no work done on the system</h2><h2>2) A) Using a lever to lift 100 newtons up to 4 meters on to a shelf</h2><h2 /><h2>3) P = 140 W</h2><h2>4) D) In a closed system, a system that isolated from its surrounds, the total energy of the system is conserved</h2>

Explanation:

1) As we know that work done is the product of force and the displacement of the point of action where force is applied

So here we have

$W = 0$

as there is no displacement in the direction where the force is applied

2)As we know that work is product of force and displacement

So we will have

$W_1 = 100 \times 4 = 400 J$

$W_2 = 200 \times 1 = 200 J$

$W_1 = 200 \times 1 = 200 J$

$W_1 = 100 \times 3 = 300 J$

So maximum work is done on

A) Using a lever to lift 100 newtons up to 4 meters on to a shelf

3)

As we know that power is rate of work done

so we have

$P = \frac{W}{t}$

$P = \frac{420}{3}$

$P = 140 W$

4)

As per energy conservation we know that

D) In a closed system, a system that isolated from its surrounds, the total energy of the system is conserved

5 0

3 years ago

Five metal samples, with equal masses, are heated to 200oC. Each solid is dropped into a beaker containing 200 ml 15oC water. Wh

Ksju [112]

Part 1) Which metal will cool the fastest?
To answer this question, we should have a look at the formula of the heat flow rate, which says "how fast" a material is able to heat/cool:
$\frac{\Delta Q}{\Delta t} = -k \frac{A \Delta T}{x}$
where:
$\Delta Q$ is the heat exchanged
$\Delta t$ is the time interval
k is thermal conductivity of the material
A the surface where the exchange of heat occurs
$\Delta T$ the variation of temperature
x is the thickness of the material
We see that the heat flow rate $\frac{\Delta Q}{\Delta t}$ is linearly proportional to k, the thermal conductivity of the material. So, the larger k, the fastest the metal will cool.
If we have a look at the thermal conductivity of each metal, we find:
- Aluminium: 237 W/(mK)
- Copper: 401 W/(mK)
- Gold: 314 W/(mK)
- Platinum: 69 W/(mK)
Therefore, copper is the material with highest heat flow rate, so the metal which cools fastest.

Part 2) Which sample of copper demonstrates the greatest increase in temperature
To solve this part, we can have a look at how the amount of heat exchanged Q is related to the increase in temperature $\Delta T$ :
$Q=m C_S \Delta T$
where m is the mass and Cs the specific heat of the material. Re-arranging the formula, we get
$\Delta T= \frac{Q}{m C_s}$
therefore, we see that the increase in temperature is inversely proportional to the mass m. This means that the block that will show the largest increase in temperature is the block with the smallest mass, so the correct answer is A) 0.5 kg.

4 0

4 years ago