Concept explainers
Review. A small object with mass 4.00 kg moves counterclockwise with constant angular speed 1.50 rad/s in a circle of radius 3.00 m centered at the origin. It starts at the point with position vector
(a)
The new position vector of the object.
Answer to Problem 10.26P
The new position vector of the object is
Explanation of Solution
The mass of the object is
Formula to calculate the angle make by the small object is,
Formula to calculate the position vector of the small object is,
Here,
Substitute
Conclusion:
Therefore, new position vector of the object is
(b)
The quadrant in which the particle is located and the angle made by its position with the positive
Answer to Problem 10.26P
The object now located in the second quadrant and makes
Explanation of Solution
Form part (a), Section (1), the angle made by the position vector from the positive axis is
Since the value of angle lies between
Conclusion:
Therefore, the object now located in the second quadrant and makes
(c)
The velocity of the object.
Answer to Problem 10.26P
The velocity of the object is
Explanation of Solution
The mass of the object is
Since the velocity vector always be the perpendicular to the position vector. So, the angle that the velocity vector made by the positive axis is,
Substitute
Formula to calculate the velocity of the object is,
Here,
Substitute
Formula to calculate the velocity vector of the object is,
Substitute
Conclusion:
Therefore, the velocity vector of the object is
(d)
The quadrant in which the particle is moving.
Answer to Problem 10.26P
The object is moving in third quadrant in anticlockwise direction.
Explanation of Solution
The mass of the object is
Form part (c), Section (1), the angle made by the velocity vector from the positive axis is
Since the value of angle lies between
Conclusion:
Therefore, the object is moving in third quadrant in anticlockwise direction.
(e)
The acceleration of the object.
Answer to Problem 10.26P
The acceleration of the object is
Explanation of Solution
Since the acceleration vector always be the perpendicular to the velocity vector. So, the angle that the acceleration vector made by the positive axis is,
Substitute
Formula to calculate the acceleration of the object is,
Here,
Substitute
Formula to calculate the acceleration vector of the object is,
Substitute
Conclusion:
Therefore, the acceleration of the object is
(f)
The position, acceleration and velocity vector.
Answer to Problem 10.26P
position, acceleration and velocity vector is shown in figure (I).
Explanation of Solution
Position, velocity and acceleration is a vector quantity hence they represented by both magnitude and direction in a vector diagram.
Draw the vector diagram of the position, velocity and the acceleration.
Figure (I)
Conclusion:
Therefore, the position, acceleration and velocity vector is shown in figure (I).
(g)
The total force vector exerted on the object.
Answer to Problem 10.26P
The total force vector exerted on the object is
Explanation of Solution
Formula to calculate the force on the object is,
Conclusion:
Substitute
Therefore, the total force vector exerted on the object is
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Chapter 10 Solutions
Physics For Scientists And Engineers, Technology Update, Loose-leaf Version
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