What are the different ways the body senses its surroundings?

A basebal (radius = .036 m, mas = .145kg) is droped from rest at the top of the Empire State Building (height = 1250ft). Calcula

lora16 [44]

Answer:

a) the initial potential energy = 541.95J

b) the final kinetic energy = 87.991 J

Explanation:

Step 1: Data given

The ball has a mass of 0.145 kg and is at a height of 381m

Step 2: Calculate potential energy

The potential energy = m * g * h

with m = the mass of the ball = 0.145 kg

with g = Gravitational acceleration = 9.81 m/s²

with h = the height of the building = 381m

The potential energy = 0.145 Kg * 9.81 m/s² * 381m = 541.95 J

FD = 1/2ρCDAv²

⇒ with FD = the drag force = the force component in the direction of the flow velocity

⇒ with ρ = density of the fluid (air in our case: ρ≈1.1839 Kg/m3 at 1 atm and 25 °C)

⇒ with v = velocity of the ball

⇒ with A = reference area, which in our case is just the cross sectional area of the ball: A=πr2

⇒ with CD is the drag coefficient - a dimensionless coefficient, that in the case of a sphere, CD=0.47

Following Newton's second law:

ΣFy = may = -mg +Dv²

Here is D=1/2ρCDA ( for convenience) = 0.001172

The terminal speed we can define as the speed of the ball where ay = 0

Therefore: -mg + Dvt² = 0

⇒vt = √(mg/D)

vt = √(0.145 * 9.8 / 0.001172) ≈ 34.837

Uinitial=mgh≈541.951 J (see first question)

Kfinal=1/2*mvt²=(m²g)/2D ≈ 87.991 J

The final kinetics energy is 87.991 J

4 0

4 years ago

A certain gas is compressed adiabatically. The amount of work done on the gas is 800 J. What is the change in the internal (ther

Black_prince [1.1K]

Answer:

800J

Explanation:

Using the formula for change in the internal energy of a system

∆U = Q - W

Q = heat added to the system

W =workdone by system.

We know the process is an adiabatic one then, there no addition/ removal of heat, then Q= 0

(∆U = -W )

Then substitute for W, we have

∆U = -[-800]

∆U= 800J

∆U = 800J

4 0

3 years ago

One strategy in a snowball fight is to throw a snowball at a high angle over level ground. Then, while your opponent is watching

agasfer [191]

Answer:

22.5°

Explanation:

Short answer: The trajectories will hit the same target when the projectile is launched at complementary angles. The second angle is 90° -67.5° = 22.5°.

__

Longer answer: The horizontal speed of the snowball launched at angle α with speed s is ...

vh = s·cos(α)

Then the horizontal distance at time t is ...

x = vh·t

and the time taken to get to some distance x is ...

t = x/vh = x/(s·cos(α))

The equation for the vertical motion of the projectile is ...

y = -4.9t² +s·sin(α)·t

Substituting the above expression for t, we have y in terms of x:

y = -4.9x²/(s·cos(α))² +(s·sin(α)·x)/(s·cos(α))

Factoring gives ...

y = (x/(cos(α))(-4.9x/(s²·cos(α)) +sin(α))

The height y will be zero at x=0 and at ...

0 = -4.9x/(s²·cos(α)) +sin(α)

x = s²·sin(α)·cos(α)/4.9 = (s²/9.8)sin(2α)

So, for some alternate angle β, we want ...

sin(2α) = sin(2β)

We know this will be the case for ...

2β = 180° -2α

β = 90° -α

The second snowball should be thrown at an angle of 90°-67.5° = 22.5° to make it hit the same point as the first.

3 0

3 years ago

yami pours powdered cocoa mix into milk and stirs it. then she microwaves the mixture for three minutes. when she takes the cup

MrRa [10]

Convection can best be observed as she blows the warm steam air that rises.

As the warm steam rises, she forces displaces it with cool air from her mouth. Because the warm steam is less dense it rises and because the cool air is more dense, it displaces the warm air.

This scenario is an example of convection.

6 0

3 years ago

Read 2 more answers

1. A particle is projected vertically upwards with a velocity of 30 ms from a point 0. Find (a) the maximum height reached(b) th

Bogdan [553]

Assuming the particle is in free fall once it is shot up, its vertical velocity v at time t is

v = 30 m/s - g t

where g = 9.8 m/s² is the magnitude of the acceleration due to gravity, and its height y is given by

y = (30 m/s) t - 1/2 g t ²

(a) At its maximum height, the particle has 0 velocity, which occurs for

0 = 30 m/s - g t

t = (30 m/s) / g ≈ 3.06 s

at which point the particle's maximum height would be

y = (30 m/s) (3.06 s) - 1/2 g (3.06 s)² ≈ 45.9184 m ≈ 46 m

(b) It takes twice the time found in part (a) to return to 0 height, t ≈ 6.1 s.

(c) The particle falls 35 m below its starting point when

-35 m = (30 m/s) t - 1/2 g t ²

Solve for t to get a time of about t ≈ 7.1 s

7 0

3 years ago

What are the different ways the body senses its surroundings?​

What are the different ways the body senses its surroundings?