As shown in the figure, a 2.10 kg box is held at rest against a spring with a force constant k = 680 N/m that is compressed a distance d.When the box is released, it slides across a surface that is frictionless, except for a rough patch that has a coefficient of kinetic friction μk = 0.35 and is 6.0 cm in length.(a)Calculate the spring's potential energy in terms of d d2(b)Calculate the magnitude of the friction force (in N). N(c)Calculate the work done by the frictional force (in J). Be sure to include the correct sign in your answer. J(d)The speed of the box is 1.9 m/s after sliding across the rough patch. Calculate the initial compression d (in cm) of the spring. cm The diagram illustrates a block on a horizontal surface, featuring a few key components:1. **Block with Initial Velocity (v):** On the left, there is a block moving towards the right with initial velocity \( v \).2. **Rough Patch:** As the block moves, it encounters a rough patch on the surface, measuring 6.0 cm in length. This area likely introduces friction, which may slow down the block.3. **Block at Rest (v = 0):** To the right, there is another block shown in contact with a wall and a spring, where its velocity is \( v = 0 \).4. **Equilibrium Position and Displacement (d):** The point labeled as the equilibrium position is an important marker in the diagram. The displacement \( d \) indicates the distance the block compresses the spring from this equilibrium position.The setup is likely used to study motion dynamics, energy loss due to friction, or the behavior of the block-spring system, such as potential and kinetic energy transformations.

Given: mass of box=2.10 kg length of rough surface = 6cm =0.06m coefficient of friction of rough…

Answered: As shown in the figure, a 2.10 kg box…

College Physics

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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As shown in the figure, a 2.10 kg box is held at rest against a spring with a force constant k = 680 N/m that is compressed a distance d.

When the box is released, it slides across a surface that is frictionless, except for a rough patch that has a coefficient of kinetic friction μ_k = 0.35 and is 6.0 cm in length.

(a)

Calculate the spring's potential energy in terms of d

d²

(b)

Calculate the magnitude of the friction force (in N).

(c)

Calculate the work done by the frictional force (in J). Be sure to include the correct sign in your answer.

(d)

The speed of the box is 1.9 m/s after sliding across the rough patch. Calculate the initial compression d (in cm) of the spring.

The diagram illustrates a block on a horizontal surface, featuring a few key components:

1. **Block with Initial Velocity (v):** On the left, there is a block moving towards the right with initial velocity \( v \).

2. **Rough Patch:** As the block moves, it encounters a rough patch on the surface, measuring 6.0 cm in length. This area likely introduces friction, which may slow down the block.

3. **Block at Rest (v = 0):** To the right, there is another block shown in contact with a wall and a spring, where its velocity is \( v = 0 \).

4. **Equilibrium Position and Displacement (d):** The point labeled as the equilibrium position is an important marker in the diagram. The displacement \( d \) indicates the distance the block compresses the spring from this equilibrium position.

The setup is likely used to study motion dynamics, energy loss due to friction, or the behavior of the block-spring system, such as potential and kinetic energy transformations.

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