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2 years ago

Calculate the kinetic energy of Julie, a 60 kg biker, traveling at a velocity of 8 m/s to the right

Physics

1 answer:

Vadim26 [7]2 years ago

8 0

Answer:

1,920 Joules

Explanation:

K.E. = 1/2 mv2

so K.E. = 1/2 (60)(8x8) = 1,920 Joules

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A hot air balloon is on the ground, 200 feet from an observer. The pilot decides to ascend at 100 ft/min. How fast is the angle

liq [111]

Answer:

0.0031792338 rad/s

Explanation:

$\theta$ = Angle of elevation

y = Height of balloon

Using trigonometry

$tan\theta=y\dfrac{y}{200}\\\Rightarrow y=200tan\theta$

Differentiating with respect to t we get

$\dfrac{dy}{dt}=\dfrac{d}{dt}200tan\theta\\\Rightarrow \dfrac{dy}{dt}=200sec^2\theta\dfrac{d\theta}{dt}\\\Rightarrow 100=200sec^2\theta\dfrac{d\theta}{dt}\\\Rightarrow \dfrac{d\theta}{dt}=\dfrac{100}{200sec^2\theta}\\\Rightarrow \dfrac{d\theta}{dt}=\dfrac{1}{2}cos^2\theta$

Now, with the base at 200 ft and height at 2500 ft

The hypotenuse is

$h=\sqrt{200^2+2500^2}\\\Rightarrow h=2507.98\ ft$

Now y = 2500 ft

$cos\theta=\dfrac{200}{h}\\\Rightarrow cos\theta=\dfrac{200}{2507.98}=0.07974$

$\dfrac{d\theta}{dt}=\dfrac{1}{2}\times 0.07974^2\\\Rightarrow \dfrac{d\theta}{dt}=0.0031792338\ rad/s$

The angle is changing at 0.0031792338 rad/s

6 0

3 years ago

A toroidal coil of N turns has a central radius b and a square cross section of side a. Find its self-inductance.

Xelga [282]

Answer:

$L = \frac{\mu_0 N^2 (a^2)}{2\pi b}$

Explanation:

As we know that magnetic field due to torroid is given as

$B = \frac{\mu_0 N i}{2\pi b}$

this is approximately constant magnetic field along the axis of the torroid

now the flux linked with one coil of the torroid is given as

$\phi = B.A$

$\phi = \frac{\mu_0 N i}{2\pi b}(a^2)$

now total flux of N number of coils is given as

$\phi_{total} = \frac{\mu_0 N^2 i(a^2)}{2\pi b}$

now we know that self inductance is the property of coil in which flux of the coil will link with the current in the coil

So we know that

$L = \frac{\phi}{i}$

$L = \frac{\mu_0 N^2 (a^2)}{2\pi b}$

3 0

3 years ago

A car's bumper is designed to withstand a 5.04 km/h (1.4-m/s) collision with an immovable object without damage to the body of t

emmasim [6.3K]

Answer:

the magnitude of the average force on the bumper is 3189.8 N

Explanation:

Given the data in the question;

In terms of force and displacement, work done is;

W = $F^>$ × $x^>$

W = $Fxcos\theta$ ------- let this be equation 1

where F is force applied, x is displacement and θ is angle between force and displacement.

Now, since the displacement of the bumper and force acting on it is in the same direction,

hence, θ = 0°

we substitute into equation 1

W = $Fxcos($ 0° $)$

W = $Fx$ ------- let this be equation 2

Now, using work energy theorem,

total work done on the system is equal to the change in kinetic energy of the system.

$W_{net$ = ΔKE

= $\frac{1}{2}$ mv² - $\frac{1}{2}$ mu² --------- let this be equation 3

where m is mass of object, v is final velocity, u is initial velocity.

from equation 2 and 3

$Fx$ = $\frac{1}{2}$ mv² - $\frac{1}{2}$ mu²

we make F, the subject of formula

F = $\frac{m}{2x}$ ( v² - u² )

given that mass of car m = 830 kg, x = 0.255 m, v = 0 m/s, and u = 1.4 m/s

so we substitute

F = $\frac{830}{(2)(0.255)}$ ( (0)² - (1.4)² )

F = 1627.45098 ( 0 - 1.96 )

F = 1627.45098 ( - 1.96 )

F = -3189.8 N

The negative sign indicates that the direction of the force was in opposite compare to the direction of the velocity of the car.

Therefore, the magnitude of the average force on the bumper is 3189.8 N

6 0

2 years ago

What temperature does water freeze at in celsius and fahrenheit?

andre [41]

32 degrees Fahrenheit
And
0 degrees Celsius

4 0

3 years ago

Read 2 more answers

If you apply a 500N force to a car 200N car for 10 seconds but it doesn't move. How much work was done on the car?

djyliett [7]

Answer:

bbx

Explanation:

xbb

3 0

2 years ago