A 3 kg block is sliding down a frictionless incline of 30 degrees. What is the a

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Question: A 3 kg block is sliding down a frictionless incline of 30 degrees. What is the acceleration of the block?

Options:

Correct Answer: 3.9 m/s²

Solution:

The acceleration down the incline is given by a = g * sin(θ) = 9.8 m/s² * sin(30°) = 4.9 m/s².

A 3 kg block is sliding down a frictionless incline of 30 degrees. What is the acceleration of the block?

A 3 kg block is sliding down a frictionless incline of 30 degrees. What is the acceleration of the block?

Correct Answer: 4.9 m/s²

Step 1: Identify the mass of the block, which is 3 kg. This information is not needed for calculating acceleration but is part of the problem.
Step 2: Identify the angle of the incline, which is 30 degrees.
Step 3: Recall the acceleration due to gravity, which is approximately 9.8 m/s².
Step 4: Use the formula for acceleration down an incline: a = g * sin(θ).
Step 5: Calculate sin(30°). The value of sin(30°) is 0.5.
Step 6: Substitute the values into the formula: a = 9.8 m/s² * 0.5.
Step 7: Perform the multiplication: a = 4.9 m/s².
Step 8: Conclude that the acceleration of the block down the incline is 4.9 m/s².

Inclined Plane Dynamics – Understanding how gravity affects an object sliding down an incline, specifically calculating acceleration using the angle of the incline.
Trigonometric Functions – Applying the sine function to determine the component of gravitational force acting along the incline.