Question

a tractor of mass m applies a force f₁ to push a block of mass m (where m < m). under which conditions will f₂, the force with which the block pushes on the tractor, be equal to f₁?
a the tractor and block must be at rest.
b the tractor and block must be moving with constant velocity.
c the tractor and block must be either at rest or moving with constant velocity.
d these two forces are always equal under all conditions.

Explanation:

To determine when \( F_1 \) (tractor on block) and \( F_2 \) (block on tractor) are equal, we use Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. These two forces are an action - reaction pair. Newton's Third Law holds regardless of the state of motion (whether at rest, moving with constant velocity, or accelerating) as long as the forces are an action - reaction pair.

• Option A: The tractor and block don't have to be at rest. Even when moving, the action - reaction forces still hold. So A is incorrect.
• Option B: They don't have to be moving with constant velocity. Even during acceleration, the magnitudes of the action - reaction forces are equal. So B is incorrect.
• Option C: The condition of being at rest or moving with constant velocity is related to Newton's First Law (equilibrium), but Newton's Third Law is about action - reaction pairs and is independent of the state of motion. So C is incorrect.
• Option D: By Newton's Third Law, the force the tractor exerts on the block (\( F_1 \)) and the force the block exerts on the tractor (\( F_2 \)) are always equal in magnitude and opposite in direction, regardless of the motion state (rest, constant velocity, acceleration). So D is correct.

Answer:

D. These two forces are always equal under all conditions.