
Concept explainers
(a)
The analysis model that describes the horizontal motion of the protons above the plane.
(a)

Answer to Problem 32P
The particle under constant velocity describes the horizontal motion of the protons above the plane.
Explanation of Solution
Figure 1 represents a proton is projected with an angle of
Write the expression for horizontal component of motion of the proton.
Here,
There is no force acting on the proton in the horizontal direction, thus the particle under constant velocity describes the horizontal motion of the protons above the plane.
Conclusion:
Therefore, the particle under constant velocity describes the horizontal motion of the protons above the plane
(b)
The analysis model that describes the vertical motion of the protons above the plane.
(b)

Answer to Problem 32P
The particle under constant acceleration describes the vertical motion of the protons above the plane.
Explanation of Solution
Write the expression for vertical component of motion of the proton.
Here,
From the above equation it is clear that the vertical component of the velocity depends only on acceleration due to gravity. The acceleration due to gravity has a constant value throughout the motion, thus the particle under constant acceleration describes the vertical motion of the protons above the plane.
Conclusion:
Therefore, the particle under constant acceleration describes the vertical motion of the protons above the plane.
(c)
Whether the Equation 3.16 be applicable to the protons.
(c)

Answer to Problem 32P
Yes, the Equation 3.16 is applicable to the protons. The proton moves in a parabolic path.
Explanation of Solution
Given that the electric field is
The vertical acceleration caused by the constant electric force
This vertical acceleration makes the proton to move in a parabolic path, this is similar to a projectile in a gravitational field.
Conclusion:
Therefore, the Equation 3.16 is applicable to the protons. The proton moves in a parabolic path.
(d)
The expression for range
(d)

Answer to Problem 32P
The expression for range
Explanation of Solution
Write the expression for vertical acceleration.
Here,
Write the expression for range from Equation 3.16.
Here,
Since the vertical acceleration is greater than acceleration due to gravity, consider vertical acceleration in the place of acceleration due to gravity.
Apply the above condition in equation (II)
Conclusion:
Substitute
Therefore, the expression for range
(e)
The two possible values of the angle
(e)

Answer to Problem 32P
The two possible values of the angle
Explanation of Solution
From subpart (d) the expression for range
Given that the range is
Conclusion:
Substitute
The other value of
Therefore, the two possible values of the angle
(f)
The time interval during which the proton is above the plane for the two possible values of
(f)

Answer to Problem 32P
The time interval during which the proton is above the plane for the two possible values of
Explanation of Solution
Write the expression for time interval.
Here,
Conclusion:
Substitute
Substitute
Therefore, the time interval during which the proton is above the plane for the two possible values of
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Chapter 19 Solutions
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