Math Problem Statement

A horizontal force, applied to a body, is twice the force of gravity. What acceleration will the body experience in the horizontal direction? Newton's Third Law is valid for... A body is lifted upward with acceleration. Which statement is true?

Solution

Let's analyze each question in detail:


Question 3

A horizontal force is applied to a body and is twice the force of gravity. What acceleration will the body experience?

Key Idea:

  • Force F=maF = ma, and the weight mgmg represents the force of gravity.
  • The horizontal force is F=2mgF = 2mg.
  • Using Newton's second law: F=ma    a=Fm.F = ma \implies a = \frac{F}{m}.
  • Substituting F=2mgF = 2mg: a=2mgm=2g.a = \frac{2mg}{m} = 2g.

Correct Answer:

(2) 2g2g


Question 4

Newton's Third Law states that for every action, there is an equal and opposite reaction. To whom does this law apply?

Options Analysis:

  1. Two interacting bodies of any mass and shape: Correct, the law applies universally to all interacting bodies regardless of their size, mass, or form.
  2. Only two interacting material points: Incorrect, as it is not limited to material points.
  3. Inertial forces: Incorrect, as Newton's third law applies to action-reaction pairs, not inertial forces.

Correct Answer:

(1) Two interacting bodies of any mass and shape.


Question 5

A body is lifted upward with acceleration. Which statement about its weight is true?

Key Idea:

  • Apparent weight WapparentW_{\text{apparent}} is the normal force experienced by the object. When accelerating upward: Wapparent=m(g+a).W_{\text{apparent}} = m(g + a).
  • If a>0a > 0, Wapparent>mgW_{\text{apparent}} > mg (weight appears greater than the gravitational force).

Options Analysis:

  1. Weight equals zero: Incorrect, this would only occur in free fall (a=ga = -g).
  2. Weight is greater than the force of gravity: Correct, due to the upward acceleration adding to gravity.
  3. Weight is less than the force of gravity: Incorrect, this would occur if accelerating downward.
  4. Weight equals the force of gravity: Incorrect, this only occurs if there is no acceleration (a=0a = 0).
  5. None of the above: Incorrect, as (2) is true.

Correct Answer:

(2) Weight is greater than the force of gravity.


Final Answers:

  • Question 3: (2) 2g2g
  • Question 4: (1) Two interacting bodies of any mass and shape.
  • Question 5: (2) Weight is greater than the force of gravity.

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Math Problem Analysis

Mathematical Concepts

Newton's Laws of Motion
Gravitational Force
Acceleration

Formulas

Force: F = ma
Gravitational Force: F_gravity = mg
Apparent Weight: W_apparent = m(g + a)

Theorems

Newton's Second Law
Newton's Third Law

Suitable Grade Level

Grades 9-12