# Tutor profile: Dalia M.

## Questions

### Subject: Physics (Newtonian Mechanics)

Barron’s AP Physics A book rests on top of a table. Which of the following are an action-reaction pair described by Newton’s third? Select two correct answers. (A) The weight of the book and the normal force of the table upon the book (B) The weight of the book and the weight of the table (C) The weight of the table and the upward pull of the table on Earth (D) The normal force upon the book from the table and the downward force on the table due to the book

(C) The weight of the table and the upward pull of the table on Earth (D) The normal force upon the book from the table and the downward force on the table due to the book Newton’s third law states that: If an object A exerts a force on object B, then object B must exert a force of equal magnitude and opposite direction back on object A Analyzing the case in choice (A), you find that the weight of the book is caused by the Earth So the action-reaction pair in this case is between the book and the earth, the table isn’t involved in that pair Analyzing the case in choice (B), both the weight of the book and the weight of the table are caused by the earth, they aren’t a pair of forces of the same magnitude and opposite direction While in the cases described in the choices (C) and (D), represents a pair of action-reaction forces between objects A and B The weight of the table caused by the earth, and the pull of the earth caused by the table The normal force exerted by the table on the book, and the downward force exerted by the book on the table

### Subject: Calculus

AP Calculus AB Let g be a twice-differentiable function with g^' (x)>0 and g^'' (x)>0 for all real numbers x, such that g(4)=12 and g(5)=18. Of the following, which is a possible value for (6) ? (A) 15 (B) 18 (C) 21 (D) 24 (E) 27

(E) 27 As g^' (x)>0, then the function g is increasing As g^'' (x)>0, then the function g is concave up Then the function g is increasing at an increasing rate And as g(4)=12 and g(5)=18, then the slope m of the function is given by: m=(18-12)/(5-4)=6 Then the slope as x changes from 5 to 6 must be more than 6 Then the only possible value for g(6) is 27

### Subject: Physics

Barron’s AP Physics What is the instantaneous power due to the gravitational force acting on a 3-kilogram projectile the instant the projectile is traveling with a velocity of 10 meters per second at an angle of 30 degree above the horizontal? (A) 300 W (B) 150 W (C) -150 W (D) -300 W

(C) -150 W Power is given by the formula: P=W/t Where W is work and t is time Work is given by the formula: W=Fd cosθ Where F is the force, d is the displacement in the direction of force, and θ is the angle between the displacement and the force As the force we are dealing with is the gravitational force which acts vertically downward, break it into its components in the direction of the displacement As the projectile is traveling at an angle of 30 degree above the horizontal Then the component of force that acts in the same direction is mg sin30° in the opposite direction of the displacement As the angle is measured from the positive x-axis Then the force is given by: mg sin(30+180)=mg sin(210°) So, W=Fd cosθ=mg sin(210°)×d And the power is: P=W/t=(mg sin(210°)×d)/t As the term d/t defines the velocity Then P= mg sin(210°)×v=3×9.8×(-1/2)×10=-147≅-150 W

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