A 35 kg sled slides along a horizontal surface on which the coefficient of kinetic friction is 0.25. Its velocity at point A is 10.0 m/s, and its velocity at point B is 2.0 m/s. You must use Work/Energy methods (not Kinematics). (a) What is the frictional force acting on the sled? (b) How much work is done on the sled by friction over the displacement ∆x = xB − xA? (c) What is the distance the sled travels between A and B?

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A 35 kg sled slides along a horizontal surface on which the coefficient of kinetic friction is 0.25. Its velocity at point A is 10.0 m/s, and its velocity at point B is 2.0 m/s. You must use Work/Energy methods (not Kinematics).

(a) What is the frictional force acting on the sled?

(b) How much work is done on the sled by friction over the displacement ∆x = xB − xA?

(c) What is the distance the sled travels between A and B?

### Motion of a Block on a Horizontal Surface

The diagram illustrates a block of mass \( m \) moving on a horizontal surface. The forces acting on the block and its displacement are represented as follows:

1. **Forces Acting on the Block:**
    - **Normal Force (\( F_N \))**: This is the force exerted by the surface on the block in the upward direction, perpendicular to the surface.
    - **Gravitational Force (\( F_g \))**: This is the force exerted by the Earth on the block in the downward direction, equal to the weight of the block \( (mg) \).
    - **Kinetic Friction Force (\( f_k \))**: This is the force exerted by the surface on the block opposing its motion, pointing to the left.

2. **Displacement (\( \Delta x \))**:
    - The block moves from point \( A \) to point \( B \) on the horizontal surface.
    - \( \Delta x \) is the vector representing the displacement from \( A \) to \( B \), where \( \Delta x \) is the distance traveled in a direction parallel to the surface.

The diagram uses arrows to indicate the direction of these forces and displacement:
- The normal force \( F_N \) is shown as an upward arrow.
- The gravitational force \( F_g \) is shown as a downward arrow.
- The kinetic friction force \( f_k \) is shown as an arrow pointing to the left.
- The displacement \( \Delta x \) is represented by a red arrow pointing to the right from point \( A \) to point \( B \).

This diagram helps in understanding the dynamics of the block moving on a horizontal surface and how different forces interact during its motion.
Transcribed Image Text:### Motion of a Block on a Horizontal Surface The diagram illustrates a block of mass \( m \) moving on a horizontal surface. The forces acting on the block and its displacement are represented as follows: 1. **Forces Acting on the Block:** - **Normal Force (\( F_N \))**: This is the force exerted by the surface on the block in the upward direction, perpendicular to the surface. - **Gravitational Force (\( F_g \))**: This is the force exerted by the Earth on the block in the downward direction, equal to the weight of the block \( (mg) \). - **Kinetic Friction Force (\( f_k \))**: This is the force exerted by the surface on the block opposing its motion, pointing to the left. 2. **Displacement (\( \Delta x \))**: - The block moves from point \( A \) to point \( B \) on the horizontal surface. - \( \Delta x \) is the vector representing the displacement from \( A \) to \( B \), where \( \Delta x \) is the distance traveled in a direction parallel to the surface. The diagram uses arrows to indicate the direction of these forces and displacement: - The normal force \( F_N \) is shown as an upward arrow. - The gravitational force \( F_g \) is shown as a downward arrow. - The kinetic friction force \( f_k \) is shown as an arrow pointing to the left. - The displacement \( \Delta x \) is represented by a red arrow pointing to the right from point \( A \) to point \( B \). This diagram helps in understanding the dynamics of the block moving on a horizontal surface and how different forces interact during its motion.
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