A 20 kg girlslides down a frictionless slide at a playground. The surface of the slide is 12.8o to the horizontal. What is her acceleration? Give your answer to one decimal place.

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BlackTom AI · Accepted Answer

We start by identifying the physics of motion on a frictionless incline. On a frictionless slide, the acceleration along the plane is due to the component of gravity parallel to the surface. This is given by a = g sin(theta), where g is 9.8 m/s^2 and theta is the angle of the incline with respect to the horizontal.

First, note the angle provided: theta = 12.8 degrees. To use sin(theta), we convert or directly use the sine of that angle: sin(12.8°) ≈ 0.222.

Next, substitute into the formula: a = 9.8 m/s^2 × sin(12.8°) ≈ 9.8 × 0.222.

Carrying out the multiplication: 9.8 × 0.222 ≈ 2.1776 m/s^2.

Rounding to one decimal place as requested gives an acceleration of approximately 2.2 m/s^2 along the incline.

Additional notes:
- This calculation assumes the slide is frictionless, so no frictional force reduces the parallel component of gravity.
- The mass of the girl (20 kg) does not affect the acceleration on a frictionless incline, since both gravitational force component along the plane and the normal reaction force scale with mass, leaving a independent of m.
- If the incline were steeper (larger theta), sin(theta) would be larger and the acceleration would increase accordingly; if shallower, acceleration would decrease.

MUF0121 Physics Unit 1 - Semester 2, 2025 5.12.1 Terminal Velocity and Weight

A 20 kg girlslides down a frictionless slide at a playground. The surface of the slide is 12.8o to the horizontal. What is her acceleration? Give your answer to one decimal place.

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