As shown in the figure, a 1.5 kg box is held at rest against a spring with a force constant k = 755 N/m that is compressed a distance d. Equilibrium position rough patch '6.0 cm 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 0.40 Hk and is 6.0 cm in length. If the speed of the box is 1.6 m/s after sliding across the rough patch, determine the initial compression d (in cm) of the spring. cm

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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**Problem Description:**

As shown in the figure, a 1.5 kg box is held at rest against a spring with a force constant \( k = 755 \, \text{N/m} \) that is compressed a distance \( d \).

![Diagram]

- The diagram illustrates a scenario where a box is pushed against a compressed spring.
- The spring is in equilibrium when not compressed or extended.
- The rough patch is indicated, measuring 6.0 cm in length, and the box slides over it after release.

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 \( \mu_k = 0.40 \) and is 6.0 cm in length. If the speed of the box is 1.6 m/s after sliding across the rough patch, determine the initial compression \( d \) (in cm) of the spring.

\[ \text{Initial compression:} \ \_\_\_\_ \text{cm} \]
Transcribed Image Text:**Problem Description:** As shown in the figure, a 1.5 kg box is held at rest against a spring with a force constant \( k = 755 \, \text{N/m} \) that is compressed a distance \( d \). ![Diagram] - The diagram illustrates a scenario where a box is pushed against a compressed spring. - The spring is in equilibrium when not compressed or extended. - The rough patch is indicated, measuring 6.0 cm in length, and the box slides over it after release. 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 \( \mu_k = 0.40 \) and is 6.0 cm in length. If the speed of the box is 1.6 m/s after sliding across the rough patch, determine the initial compression \( d \) (in cm) of the spring. \[ \text{Initial compression:} \ \_\_\_\_ \text{cm} \]
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