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To the right, a box of mass 26 kg is sliding down a frictionless incline that makes an angle of 27 with the horizontal. What is the acceleration of the box?

a. 9.8 m/s²
b. 5.2 m/s²
c. 7.8 m/s²
d. 3.5 m/s²

User Luissquall
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1 Answer

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Final answer:

The acceleration of a 26 kg box sliding down a frictionless 27° incline is calculated using the component of gravitational acceleration along the incline. It is found to be approximately 4.4492 m/s², with the closest answer choice being b. 5.2 m/s².

Step-by-step explanation:

The student is asking about the acceleration of a box sliding down a frictionless incline. To find the acceleration, we use the gravitational acceleration (g) and the angle of the incline (θ).

The acceleration of the box sliding down the frictionless incline can be determined using the formula:

acceleration = g * sin(θ)

where g is the acceleration due to gravity (approximately 9.8 m/s²) and θ is the angle of the incline (27° in this case).

Substituting the values, we have:

acceleration = 9.8 m/s² * sin(27°)The component of gravitational acceleration down the incline is g sin(θ), so we calculate this with g = 9.8 m/s2 and θ = 27°. The calculation is as follows:

Acceleration, a = g sin(θ) = 9.8 sin(27°) = 9.8 * 0.4540 = 4.4492 m/s2.

Thus, the closest answer choice to the calculated acceleration is b. 5.2 m/s2.

User Zggame
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