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3 years ago

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A ball rolls from rest at the top of a 15.5 m hill, downward to the right and back upward onto a 8.25 m hill. How fast is the ba

ll moving at the top of the second hill?

1 answer:

lana66690 [7]3 years ago

6 0

Answer:

?

Explanation:

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<em>Another key factor that determines a star's colour is its temperature. As stars become hotter, the overall radiated energy increases, and the peak of the curve changes to shorter wavelengths. To put it another way, when a star heats up, the light it produces moves toward the blue end of the spectrum.</em>

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3 years ago

A particle has a charge of q = +4.9 μC and is located at the origin. As the drawing shows, an electric field of Ex = +242 N/C ex

irina1246 [14]

a)

$F_{E_x}=1.19\cdot 10^{-3}N$ (+x axis)

$F_{B_x}=0$

$F_{B_y}=0$

b)

$F_{E_x}=1.19\cdot 10^{-3} N$ (+x axis)

$F_{B_x}=0$

$F_{B_y}=3.21\cdot 10^{-3}N$ (+z axis)

c)

$F_{E_x}=1.19\cdot 10^{-3} N$ (+x axis)

$F_{B_x}=3.21\cdot 10^{-3} N$ (+y axis)

$F_{B_y}=3.21\cdot 10^{-3}N$ (-x axis)

Explanation:

a)

The electric force exerted on a charged particle is given by

$F=qE$

where

q is the charge

E is the electric field

For a positive charge, the direction of the force is the same as the electric field.

In this problem:

$q=+4.9\mu C=+4.9\cdot 10^{-6}C$ is the charge

$E_x=+242 N/C$ is the electric field, along the x-direction

So the electric force (along the x-direction) is:

$F_{E_x}=(4.9\cdot 10^{-6})(242)=1.19\cdot 10^{-3} N$

towards positive x-direction.

The magnetic force instead is given by

$F=qvB sin \theta$

where

q is the charge

v is the velocity of the charge

B is the magnetic field

$\theta$ is the angle between the directions of v and B

Here the charge is stationary: this means $v=0$ , therefore the magnetic force due to each component of the magnetic field is zero.

b)

In this case, the particle is moving along the +x axis.

The magnitude of the electric force does not depend on the speed: therefore, the electric force on the particle here is the same as in part a,

$F_{E_x}=1.19\cdot 10^{-3} N$ (towards positive x-direction)

Concerning the magnetic force, we have to analyze the two different fields:

- $B_x$ : this field is parallel to the velocity of the particle, which is moving along the +x axis. Therefore, $\theta=0^{\circ}$ , so the force due to this field is zero.

$- B_y$ : this field is perpendicular to the velocity of the particle, which is moving along the +x axis. Therefore, $\theta=90^{\circ}$ . Therefore, $\theta=90^{\circ}$ , so the force due to this field is:

$F_{B_y}=qvB_y$

where:

$q=+4.9\cdot 10^{-6}C$ is the charge

$v=345 m/s$ is the velocity

$B_y = +1.9 T$ is the magnetic field

Substituting,

$F_{B_y}=(4.9\cdot 10^{-6})(345)(1.9)=3.21\cdot 10^{-3} N$

And the direction of this force can be found using the right-hand rule:

- Index finger: direction of the velocity (+x axis)

- Middle finger: direction of the magnetic field (+y axis)

- Thumb: direction of the force (+z axis)

c)

As in part b), the electric force has not change, since it does not depend on the veocity of the particle:

$F_{E_x}=1.19\cdot 10^{-3}N$ (+x axis)

For the field $B_x$ , the velocity (+z axis) is now perpendicular to the magnetic field (+x axis), so the force is

$F_{B_x}=qvB_x$

And by substituting,

$F_{B_x}=(4.9\cdot 10^{-6})(345)(1.9)=3.21\cdot 10^{-3} N$

And by using the right-hand rule:

- Index finger: velocity (+z axis)

- Middle finger: magnetic field (+x axis)

- Thumb: force (+y axis)

For the field $B_y$ , the velocity (+z axis) is also perpendicular to the magnetic field (+y axis), so the force is

$F_{B_y}=qvB_y$

And by substituting,

$F_{B_y}=(4.9\cdot 10^{-6})(345)(1.9)=3.21\cdot 10^{-3} N$

And by using the right-hand rule:

- Index finger: velocity (+z axis)

- Middle finger: magnetic field (+y axis)

- Thumb: force (-y axis)

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3 years ago

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True because the atmosphere is in the way

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3 years ago

FIND MEFIND V AT THE FIRST HILLFIND HEIGHT OF THE SECOND HILLFIND V AT POINT A

vitfil [10]

1)

At the starting point, the spring releases potential energy which is converted to kinetic energy of the truck. The formula fr calculating the elastic potential energy of the spring is expressed as

PE = 1/2kx^2

where

x is the extension of the spring

k is the spring constant

From the information given,

k = 8500

x = 7

Thus,

PE = 1/2 x 8500 x 7^2 = 208250 J

Since elastic potential energy of spring = kinetic energy of the truck, it means that

Kinetic energy = 208250

The formula for calculating kinetic energy is expressed as

KE = 1/2mv^2

where

m = mass of truck

v = velocity of truck

From the diagram,

m = 600

Thus,

208250 = 1/2 x 600 x v^2

208250 = 300v^2

v^2 = 208250/300 = 694.17

v = square root of 694.17

v = 26.35 m/s

The velocity at which the truck is moving is 26.35 m/s

The potential energy of the truck at that point is calculated by apply the formula,

Potential energy = mgh

where

g = acceleration due to gravity and its value is 9.81 m/s

h is the height of the truck and it is 20

m is the mass of the truck and it is 600

Thus,

Potential energy = 600 x 9.81 x 20 = 117720

Mechanical energy = potential energy + kinetic energy

Mechanical energy = 208250 + 117720 = 325970 J

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1 year ago