When a bow is stretched back and an arrow is shot what type of energy conversion has occured

Learning Goal: To review the concept of conservative forces and to understand that electrostatic forces are, in fact, conservati

CaHeK987 [17]

Explanation:

The electrostatic forces are conservative forces!

The mainly property of the conservative fields is $\vec{\nabla} \times \vec E=\vec 0$

In spherical coordinates the field's expression is:

$\vec E=\frac{Q}{4\pi \epsilon _0 r^2} .\^r$

and the curl expression is:

$\nabla\times \vec E=\frac{1}{r^2{\sin}\,\theta}\left|\begin{matrix}\hat{r} & r\,\hat{\theta} & r\,{\sin}\,\theta\,\hat{\varphi} \\& & \\\frac{\partial}{\partial r} & \frac{\partial}{\partial \theta} & \frac{\partial}{\partial \varphi}\\ & & \\E_r & rE_\theta & r{\sin}\,\theta\, E_\varphi\end{matrix}\right|=(0, 0, 0)$

to find the expression for the potential function associated:

$\vec E=\vec \nabla . V, \Delta V= V_b-V_a=-\int _c \vec E.d\vec l=-\int _c E\^r.dr\^r=-\int _c Edr=\int \limits^a_b \frac{Q}{4\pi \epsilon _0 r^2} dr= \frac{Q}{4\pi \epsilon _0}.(\frac{1}{r}|^b_a)= \frac{Q}{4\pi \epsilon _0}.(\frac{1}{b}-\frac{1}{a})$

5 0

3 years ago

What uniform magnetic field, applied perpendicular to a beam

schepotkina [342]

Answer:

The magnetic field is $2.11\times10^{-5}\ T$

Explanation:

Given that,

Speed $v=1.30\times10^{6}\ m/s$

Radius = 0.350 m

We need to calculate the magnetic field

Using formula of magnetic field

$B =\dfrac{mv}{qr}$

Where, m = mass of electron

v = speed of electron

q = charge of electron

r = radius

Put the value into the formula

$B=\dfrac{9.1\times10^{-31}\times1.30\times10^{6}}{1.6\times10^{-19}\times0.350}$

$B=2.11\times10^{-5}\ T$

Hence, The magnetic field is $2.11\times10^{-5}\ T$

5 0

4 years ago

Tranh slowed his skateboard as he

ICE Princess25 [194]

Answer:

Explanation:

Given parameters:

Initial velocity = 8m/s

Final velocity = 2m/s

Time taken = 3seconds

Unknown and solution:

1. Is he accelerating or decelerating?

Tranh is obviously decelerating in this period. This is negative form of acceleration in which the speed reduces as the body comes to a stop.

Deceleration is a negative change in velocity with time i.e a body is reducing its velocity as time is changing.

2. What is the value?

Mathematically;

Deceleration = $\frac{Final velocity - initial velocity}{time taken}$

Deceleration = $\frac{2 -8}{3}$

= -2m/s²

3 0

3 years ago

A kid at the junior high cafeteria wants to propel an empty milk carton along a lunch table by hitting it with a 3.0g spit ball.

Natasha_Volkova [10]

Answer:

4.3 m/s

Explanation:

Using conservation of momentum, assume that the collision is elastic and that the 3.0 g ball stuck with the carton

3.0 g = 3 / 1000 = 0.003 kg = m₁

40 g = 40 / 1000 = 0.04 kg = m₂, u₂ = 0 since the body is stationary and v = 0.3m/s

m₁u₁ + m₂u₂ = v ( m₁ + m₂)

0.003 u₁ = 0.30 ( 0.003 + 0.04) = 0.0129

u₁ = 0.0129 / 0.003 = 4.3 m/s

5 0

3 years ago

A rock is thrown from a cliff with a horizontal velocity of 12.6m/s it lands in the water below 1.45 seconds later, how high is

Nadusha1986 [10]

Answer:

The height of the cliff is 28.57 m.

Explanation:

Given;

initial velocity of the rock, u = 12.6 m/s

time of motion, t = 1.45 s

The height of the cliff is given by;

h = ut + ¹/₂gt²

h = (12.6 x 1.45) + ¹/₂(9.8)(1.45)²

h = 18.27 + 10.30

h = 28.57 m

Therefore, the height of the cliff is 28.57 m.

6 0

3 years ago