Imagine a system where a block rests on an inclined plane. The block is then given an initial push so that it starts sliding down along the plane. After traveling some distance down the inclined plane it comes to rest due to frictional forces. In the simplest case, there are three forces acting upon the motion of the block-the initial push, gravity, and friction. Which of these statements about the work done by these three forces is true?

-The work done by gravity is equal to the sum of the work done by friction and the initial push.

-All three forces contribute an equal amount of work.

-The work done by friction is equal to the sum of the work done by gravity and the initial push.

-The work done by the initial push is equal to the sum of the work done by friction and gravity.

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Physics

3 February, 09:17

Imagine a system where a block rests on an inclined plane. The block is then given an initial push so that it starts sliding down along the plane. After traveling some distance down the inclined plane it comes to rest due to frictional forces. In the simplest case, there are three forces acting upon the motion of the block-the initial push, gravity, and friction. Which of these statements about the work done by these three forces is true?

-The work done by gravity is equal to the sum of the work done by friction and the initial push.

-All three forces contribute an equal amount of work.

-The work done by friction is equal to the sum of the work done by gravity and the initial push.

-The work done by the initial push is equal to the sum of the work done by friction and gravity.

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Answers (1)

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Delilah Dickson · Answer 1

the correct affirmation is the 3

Explanation:

Let's analyze the problem with Newton's second law before looking at the claims.

X axis parallel to the plane, positive down

F - fr + Wₓ = ma

Y Axis perpendicular to the plane

N - Wy = 0

With trigonometry

Wₓ = W sin θ

Wy = w cos θ

Let's multiply by the displacement along the plane, to relate to the work, which has as expression W = F d

F d - fr d + Wx d = ma d

Push W₁ = Fd

frictional force W₂ = - fr d

gravity W₃ = Wx d

W₁ + W₃ - W₂ = m a d

Analysis affirmations:

R1) false. The work of gravity is the subtraction

R2) false. Each force contributes according to its magnitude

R3) true. In the equation we see that, if the acceleration is zero, W2 = W1 + W3

R4) False. It equals the difference

the correct affirmation is the 3