Problem 15: A cube of mass m is initially at rest at the highest point of an inclined plane which has a height of 6.63 m and has an angle of 0 = 17.7' with respect to the horizontal. After it has been released, it is found to be traveling at v= 0.19 m/s a distance d after the end of the inclined plane, as shown. The coefficient of kinetic friction between the cube and the plane is up = 0.1, and the coefficient of friction on the horizontal surface is μ = 0.2. h m Find the distance, d, in meters. d=1 m 01 X V m

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Chapter1: Units, Trigonometry. And Vectors
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**Problem 15:**

A cube of mass \( m \) is initially at rest at the highest point of an inclined plane, which has a height of \( 6.63 \, \text{m} \) and an angle of \( \theta = 17.7^\circ \) with respect to the horizontal. After it has been released, it is found to be traveling at \( v = 0.19 \, \text{m/s} \) a distance \( d \) after the end of the inclined plane, as shown. The coefficient of kinetic friction between the cube and the plane is \( \mu_p = 0.1 \), and the coefficient of friction on the horizontal surface is \( \mu_r = 0.2 \).

**Diagram Explanation:**

- The diagram shows a cube labeled \( m \) at the bottom of an inclined plane.
- The inclined plane has height \( h \) and angle \( \theta \) with respect to the horizontal.
- After traveling down the incline, the cube slides a distance \( d \) along a horizontal surface with velocity \( v \).

**Task:**

Find the distance \( d \), in meters.

**Calculation Input:**

- An input box for entering the calculated distance \( d \).
- A calculator interface with trigonometric functions, allowing input using either degrees or radians.

**Note:** The problem requires considering the effects of friction on both the inclined plane and the horizontal surface.
Transcribed Image Text:**Problem 15:** A cube of mass \( m \) is initially at rest at the highest point of an inclined plane, which has a height of \( 6.63 \, \text{m} \) and an angle of \( \theta = 17.7^\circ \) with respect to the horizontal. After it has been released, it is found to be traveling at \( v = 0.19 \, \text{m/s} \) a distance \( d \) after the end of the inclined plane, as shown. The coefficient of kinetic friction between the cube and the plane is \( \mu_p = 0.1 \), and the coefficient of friction on the horizontal surface is \( \mu_r = 0.2 \). **Diagram Explanation:** - The diagram shows a cube labeled \( m \) at the bottom of an inclined plane. - The inclined plane has height \( h \) and angle \( \theta \) with respect to the horizontal. - After traveling down the incline, the cube slides a distance \( d \) along a horizontal surface with velocity \( v \). **Task:** Find the distance \( d \), in meters. **Calculation Input:** - An input box for entering the calculated distance \( d \). - A calculator interface with trigonometric functions, allowing input using either degrees or radians. **Note:** The problem requires considering the effects of friction on both the inclined plane and the horizontal surface.
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