What is the acceleration of a 5.00 kg block standing on a frictionless 30.0º inclined plane? m = ?

A
8.49 s2

B
24.5 s2

C
4.90 s2

D
9.80 s2

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Question

For an object on a frictionless incline, which component of its weight is responsible for its acceleration down the plane, and how is it calculated?

Answer

The component parallel to the incline, calculated as m*g*sin(θ)

Question

Using Newton's Second Law (F_net = m*a), derive the formula for the acceleration (a) of an object on a frictionless incline of angle θ. Show why the mass (m) cancels out.

Answer

The net force down the incline is F_parallel = m*g*sin(θ). Setting this equal to m*a gives m*a = m*g*sin(θ). Dividing both sides by m yields a = g*sin(θ). The mass cancels, showing the acceleration is independent of it.

Question

On a frictionless 30° incline, an object accelerates at 4.90 m/s². If the incline angle is increased to 60°, would the acceleration increase, decrease, or stay the same? Calculate the new acceleration (use g = 9.80 m/s²).

Answer

It would increase. The new acceleration would be a = g*sin(60°) = 9.80 * 0.866 ≈ 8.49 m/s².

Question

What is the magnitude and direction of the other component of the weight (the one perpendicular to the incline)? What force balances it for an object remaining on the surface?

Answer

It is m*g*cos(θ), directed perpendicularly into the incline. It is balanced by the normal force exerted by the surface, which is equal in magnitude and opposite in direction.

Question

In this problem, the mass (5.00 kg) was given but not needed to find the acceleration. Describe a scenario involving an inclined plane where you would need to know the object's mass to solve the problem.

Answer

You would need the mass if calculating a force, such as the gravitational force down the incline (F_parallel = m*g*sinθ), the normal force (F_n = m*g*cosθ), or if friction were present (as the frictional force μ*m*g*cosθ depends on mass).

Mini Quiz

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Does the acceleration of an object sliding down a frictionless inclined plane depend on its mass?

What is the acceleration of a 5.00 kg block standing on a frictionless 30.0º inclined plane? m = ?

A
8.49 s2

B
24.5 s2

C
4.90 s2

D
9.80 s2

The acceleration of the block on the inclined plane depends on the gravitational acceleration and the angle of the incline.

Topic Flashcards

Mini Quiz

Related Questions

What is the acceleration of a 5.00 kg block standing on a frictionless 30.0º inclined plane? m = ?

A 8.49 s2 B 24.5 s2 C 4.90 s2 D 9.80 s2

The acceleration of the block on the inclined plane depends on the gravitational acceleration and the angle of the incline.

Topic Flashcards

Mini Quiz

Related Questions

A
8.49 s2

B
24.5 s2

C
4.90 s2

D
9.80 s2