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 , and the weight represents the force of gravity.
- The horizontal force is .
- Using Newton's second law:
- Substituting :
Correct Answer:
(2)
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:
- Two interacting bodies of any mass and shape: Correct, the law applies universally to all interacting bodies regardless of their size, mass, or form.
- Only two interacting material points: Incorrect, as it is not limited to material points.
- 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 is the normal force experienced by the object. When accelerating upward:
- If , (weight appears greater than the gravitational force).
Options Analysis:
- Weight equals zero: Incorrect, this would only occur in free fall ().
- Weight is greater than the force of gravity: Correct, due to the upward acceleration adding to gravity.
- Weight is less than the force of gravity: Incorrect, this would occur if accelerating downward.
- Weight equals the force of gravity: Incorrect, this only occurs if there is no acceleration ().
- 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)
- 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