Question

1. Mass is defined as______________________________________; the unit is _______________ ( ___ ) 2. Force is defined as_______________________________________, the unit is ______________ ( ___ )
Is weight considered mass or force? ________
3. How do you calculate Force (weight) of an apple falling on the y axis?________________________ 4. How do you calculate Force of the apple rolling on the x axis?______________________________ 5. A small dwarf and a strong woodsman are pushed off a ledge:
a. Who would land first?_____________________
b. Who will hit the ground hardest, with a greater force? _________________________
c. What is the difference between the rate of falling and the force of an object landing?
________________________________________________________________________

Answer 1

1. Mass is defined as the amount of matter in an object (a measure of its inertia); the unit is kilogram (kg).

2. Force is defined as an interaction that causes an object to accelerate (quantified by Newton’s second law F = m·a); the unit is newton (N).
Is weight considered mass or force? Weight is a force.

3. Force (weight) of an apple falling on the y axis: F_y = m·g (downwards). With g ≈ 9.8 m/s², F_y = m·9.8 N (or vector: F_y = −m g if +y is upward).

4. Force of the apple rolling on the x axis: use F_x = m·a_x.
- If it rolls at constant speed, a_x = 0 so F_x = 0 (no net horizontal force).
- If friction/drag is causing deceleration, F_x = −m·(deceleration) (or you can model friction as F_f ≈ μ·N ≈ μ·m·g for simple cases).
- If rolling down an incline, the driving component is F_x = m g sinθ.

5. A small dwarf and a strong woodsman pushed off a ledge:
a. Who would land first? — If air resistance is negligible, they land at the same time (same acceleration g). With significant air resistance, shape and area can change fall time.
b. Who will hit the ground hardest, with a greater force? — Typically the heavier woodsman will exert a greater impact force because he has more momentum/weight; but the exact impact force depends on how quickly they are brought to rest (F ≈ Δp/Δt or from energy: larger kinetic energy and shorter stopping distance → larger force).
c. What is the difference between the rate of falling and the force of an object landing? — The rate of falling refers to acceleration due to gravity (how quickly velocity increases, ≈9.8 m/s²). The force of landing depends on mass, impact velocity, and how rapidly the object is stopped (F = m·a during deceleration or F ≈ Δp/Δt); so two objects can fall at the same rate but produce different impact forces because of different masses or stopping times/distances.