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Yuki888 [10]
3 years ago
11

A proton travels with a speed of 5.05 ✕ 106 m/s at an angle of 64° with the direction of a magnetic field of magnitude 0.160 T i

n the positive x-direction.(a) What is the magnitude of the magnetic force on the proton? N
(b) What is the proton's acceleration? m/s2
Physics
2 answers:
Natali [406]3 years ago
7 0

Answer:

(a) the magnitude of the magnetic force on the proton is 1.16 x 10⁻¹³ N

(b) the proton's acceleration is 6.97 x 10¹³ m/s²

Explanation:

given information:

proton's speed, v =  5.05 ✕ 10⁶ m/s

angle, θ = 64°

magnetic field, B = 0.160 T ( +x direction)

(a) the magnitude of the magnetic force on the proton

F = q v B sin θ

where

F = magnetic force (N)

q = charge (C)

v = speed (m/s)

B = magnetic field (T)

θ = angle

F = q v B sin θ

proton charge, q = 1.602 x 10⁻¹⁹ C

thus,

F = (1.602 x 10⁻¹⁹) (5.05 ✕ 10⁶) (0.160) sin 64°

  = 1.16 x 10⁻¹³ N

the proton's acceleration

F = m a

where

m = mass (kg)

a = acceleration (m/s²)

the mass of proton, m = 1.67 x 10⁻²⁷ kg

so,

F = m a

a = F/m

  = (1.16 x 10⁻¹³)/(1.67 x 10⁻²⁷)

  = 6.97 x 10¹³ m/s²

Setler [38]3 years ago
4 0

Answer:

A. 1.19 * 10^(-13) N

B. 7.12 * 10^(15) m/s²

Explanation:

Parameters given:

Speed, v = 5.05 * 10^6 m/s

Angle, A = 64°

Magnetic field strength, B = 0.160T

Mass of proton, m = 1.673 * 10^(-27) kg

Charge of proton, q = 1.6023 * 10^(-19) C

A. Magnetic force is given as:

F = q*v*B*sinA

F = 1.6023 * 10^(-19) * 5.05 * 10^6 * 0.160 * sin64

F = 1.19 * 10^(-13) N

B. Force is generally given as:

F = m*a

Hence, we can find acceleration, a, by making it the subject of formula:

a = F/m

a = (1.19 * 10^(-13))/(1.673 * 10^-27)

a = 7.12 * 10^15 m/s²

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Taking into account the definition of kinetic, potencial and mechanical energy, when the brick hits the ground, it has a speed of 7,668 m/s.

<h3>Kinetic energy</h3>

Kinetic energy is a form of energy. It is defined as the energy associated with bodies that are in motion and this energy depends on the mass and speed of the body.

Kinetic energy is defined as the amount of work necessary to accelerate a body of a given mass and at rest, until it reaches a given speed. Once this point is reached, the amount of accumulated kinetic energy will remain the same unless there is a change in speed or the body returns to its state of rest by applying a force.

The kinetic energy is represented by the following expression:

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Where:

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On the other hand, potential energy is the energy that measures the ability of a system to perform work based on its position. In other words, this is the energy that a body has at a certain height above the ground.

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The principle of conservation of mechanical energy indicates that the mechanical energy of a body remains constant when all the forces acting on it are conservative (a force is conservative when the work it does on a body depends only on the initial and final points and not the path taken to get from one to the other.)

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A brick of mass 5 kg is released from rest at a height of 3 m. Then, at this height, the brick of mass has no speed, so the kinetic energy has a value of zero because it depends on the speed or moving bodies. But the potential energy is calculated as:

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So, the mechanical energy is calculated as:

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The principle of conservation of mechanical energy  can be applied in this case. Then, when the brick hits the ground, the mechanical energy is 147 J. In this case, considering that the height is 0 m, the potential energy is zero because this energy depends on the relative height of the object. But the object has speed, so it will have kinetic energy. Then:

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Finally, when the brick hits the ground, it has a speed of 7,668 m/s.

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