A block of ice sliding without friction down a 20° slope has acceleration

Question

BlackTom AI · Accepted Answer

Consider the situation: a block on a frictionless slope experiences acceleration only along the slope due to gravity.
Option 1: 3.4 m/s2. This matches a = g sin(theta) with g ≈ 9.8 m/s2 and theta = 20°. Since sin(20°) ≈ 0.342, a ≈ 9.8 × 0.342 ≈ 3.35 m/s2, which rounds to 3.4 m/s2.
Option 2: 9.8 m/s2. This would be the full gravitational acceleration if the block were moving vertically, not along a slope. Frictionless contact on a incline reduces the effective acceleration to g sin(theta), not g.
Option 3: 2.2 m/s2. This value would correspond to a smaller factor than sin20° or an incorrect angle; it does not fit a = g sin(20°) and is thus inaccurate for this scenario.
Option 4: 4.9 m/s2. This equals g/2 and would correspond to sin(theta) ≈ 0.5, i.e., theta ≈ 30°, which is inconsistent with a 20° incline. Therefore it misrepresents the geometry of the situation.

SPHY001 Practice Quiz - Unit 05 | LA045

A block of ice sliding without friction down a 20° slope has acceleration

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