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MAVERICK [17]
3 years ago
15

Exercise 15.1 (a) Find the magnitude of the electric force between two protons separated by 1 femtometer (10^-15), approximately

the distance between two protons in the nucleus of a helium atom. (b) If the protons were not held together by the strong nuclear force, what would be their initial acceleration due to the electric force between them
Physics
1 answer:
Goryan [66]3 years ago
7 0

Answer:

(a) 230.4 N

(b) a = 1.38\times10^{29} m/s^{2}

Explanation:

Charge on a proton, q = 1.6\times10^{-19}C

Distance between the two protons, d = 1 femto meter = 1\times10^{-15}m

(a) By use of coulomb's law, the force between the two protons is given by

F =\frac{k\times q\times q}{d^{2}}

Where, k is the Coulombic constant = 9x 10^9 Nm^2/C^2

So, the force between them is given by

F =\frac{9\times10^{9}\times 1.6\times10^{-19}\times 1.6\times10^{-19}}{\left (1\times10^{-15}  \right )^{2}}

F = 230.4 N

(b) Acceleration is the ratio of force to the mass of proton.

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

So, acceleration

a=\frac{230.4}{1.67\times10^{-27}}

a = 1.38\times10^{29} m/s^{2}

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Let’s look at a radio-controlled model car. Suppose that at time t1=2.0st1=2.0s the car has components of velocity vx=1.0m/svx=1
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Answer:

a_x=6\ \text{m/s}^2 and a_y=0\ \text{m/s}^2

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t_1=2\ \text{s}

v_x=1\ \text{m/s}

v_y=3\ \text{m/s}

t_2=2.5\ \text{s}

v_x=4\ \text{m/s}

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Average acceleration in the different axes

a_x=\dfrac{\Delta v_x}{\Delta t}\\\Rightarrow a_x=\dfrac{4-1}{2.5-2}\\\Rightarrow a_x=6\ \text{m/s}^2

a_y=\dfrac{\Delta v_y}{\Delta t}\\\Rightarrow a_y=\dfrac{3-3}{2.5-2}\\\Rightarrow a_y=0\ \text{m/s}^2

The components of the acceleration is a_x=6\ \text{m/s}^2 and a_y=0\ \text{m/s}^2

The magnitude of acceleration

a=\sqrt{a_x^2+a_y^2}\\\Rightarrow a=\sqrt{6^2+0^2}\\\Rightarrow a=6\ \text{m/s}^2

Direction

\theta=\tan^{-1}\dfrac{a_y}{a_x}\\\Rightarrow \theta=\tan^{-1}\dfrac{0}{6}\\\Rightarrow \theta=0^{\circ}

The magnitude of accleration is 6\ \text{m/s}^2 and the direction is 0^{\circ}.

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