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Iteru [2.4K]
3 years ago
14

A particle with charge −− 5.90 nCnC is moving in a uniform magnetic field B⃗ =−(B→=−( 1.28 TT )k^k^. The magnetic force on the p

article is measured to be F⃗ =−(F→=−( 3.70×10−7 NN )i^+()i^+( 7.60×10−7 NN )j^)j^.
(a) Calculate all the components of the velocity of the particle that you can from this information.
(b) Are there components of the velocity that are not determined by the measurement of the force? Explain.
(c) Calculate the scalar product v⃗ ⋅F⃗ . What is the angle between v⃗ and F⃗
Physics
1 answer:
maks197457 [2]3 years ago
4 0

Answer:

Explanation:

Given that,

Charge q=-5.90nC

Magnetic field B= -1.28T k

And the magnetic force

F =−( 3.70×10−7N )i+( 7.60×10−7N )j

Let the velocity be V(xi + yj + zk)

Then, the force is given as

Note i×i=j×j×k×k=0

i×j=k. j×i=-k

j×k=i. k×j=-i

k×i=j. i×k=-j

The force in a magnetic field is given as

F= q(v×B)

−( 3.70×10−7N )i+( 7.60×10−7N )j =

q(xi + yj + zk) × -1.28k

−( 3.70×10−7N )i+( 7.60×10−7N )j=

q( -1.28x i×k - 1.28y j×k - 1.28z k×k)

−( 3.70×10−7N )i+( 7.60×10−7N )j=

q( 1.28xj - 1.28y i )

−( 3.70×10−7N )i+( 7.60×10−7N )j=

q( -1.28y i + 1.28x j)

So comparing comparing coefficients

let compare x axis component

-( 3.70×10−7N )i=-1.28qy i

−3.70×10−7N = -1.28qy

y= -3.7×10^-7/-1.28q

y= -3.7×10^-7/-1.28×-5.90×10^-9)

y=-48.99m/s

y≈-49m/s

Let compare y-axisaxis

7.6×10−7N j = 1.28qx j

7.6×10−7N = 1.28qx

x= 7.6×10^-7/1.28q

x= 7.6×10^-7/1.28×-5.90×10^-9

x=-100.64m/s

a. Then, the velocity of the x component is x= -100.64m/s

b. Also, the velocity component of the y axis is y=-49m/s

c. We will compute

V•F

V=-100.64i -49j

F=−( 3.70×10−7 N )i+( 7.60×10−7 N )j

Note

i.j=j.i=0. Also i.i = j.j =1

V•F is

(-100.64i-49j)•−(3.70×10−7N)i+(7.60×10−7 N )j =

3.724×10^-5 - 3.724×10^-5=0

V•F=0

d. Angle between V and F

V•F=|V||F|Cosx

0=|V||F|Cosx

Cosx=0

x= arccos(0)

x=90°

Since the dot product is zero, from vectors , if the dot product of two vectors is zero, then the vectors are perpendicular to each other

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One object is thrown vertically upward with an initial velocity of 100 m/s and
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We have that for the Question it can be said that The maximum height reached  by the first <em>object</em> will be  100 times  that of the other.

  • (H_{max})_1=100*(H_{max})_2

From the question we are told

One object is thrown vertically upward with an initial velocity of 100 m/s and  another object with an initial velocity of 10 m/s. The maximum height reached  by the first object will be

that of the other.

a. 10,000 times

b. none of these

<em>c. </em><em>1000 times</em>

d. 100 times

<em>e.</em><em> 10 times</em>

Generally the equation for the velocity is mathematically given as

v=\frac{d}{t}\\\\Where\\\\\frac{H_{max}_1}{H_{max}_2}=\frac{(V_1)^2}{(v_2)^2}\\\\\frac{H_{max}_1}{H_{max}_2}=\frac{10000}{(10}\\\\

(H_{max})_1=100*(H_{max})_2

Therefore

The maximum height reached  by the first <em>object</em> will be  100 times  that of the other.

(H_{max})_1=100*(H_{max})_2

For more information on this visit

brainly.com/question/23379286

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