In the following diagram, M = 5 kg, m = 3 kg and the kinetic frictional coefficient is 0.25 between the surface and the big M. The small m is 3 meters above the ground. 14. find the work done by the friction as the big M slides through a distance of 4 meters. 15. find the speed of the small m when it touches the ground. 2070 1 M MK 6m ??? m 4m //////////

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### Educational Content: Physics Problem

**Context:**
In the following diagram, a physics problem is presented involving two masses and a pulley system. The larger mass \( M = 5 \, \text{kg} \), the smaller mass \( m = 3 \, \text{kg} \), and the kinetic frictional coefficient \( \mu_k = 0.25 \) between the surface and the larger mass \( M \). The smaller mass \( m \) is initially positioned 3 meters above the ground.

**Diagram Description:**
The diagram illustrates a horizontal surface where the larger mass \( M \) rests. It is connected to a smaller mass \( m \) by a rope that passes over a pulley. The rope is assumed to be massless and frictionless. The smaller mass \( m \) hangs vertically, extending 3 meters upward from the ground. 

**Analysis Questions:**

**14. Find the work done by the friction as the larger mass \( M \) slides through a distance of 4 meters.**

- **Solution Approach:**
  To calculate the work done by friction, use the formula:
  \[
  \text{Work} = \text{frictional force} \times \text{distance}
  \]
  The frictional force \( = \mu_k \times M \times g \), where \( g = 9.8 \, \text{m/s}^2 \).

**15. Find the speed of the smaller mass \( m \) when it touches the ground.**

- **Solution Approach:**
  Apply the conservation of energy principle or use kinematic equations to find the speed of the smaller mass \( m \) as it descends and touches the ground.

This setup can be elaborated through equations to solve these problems quantitatively, encouraging students to apply their understanding of mechanics, involving concepts such as Newton's laws, friction, and energy conservation.
Transcribed Image Text:### Educational Content: Physics Problem **Context:** In the following diagram, a physics problem is presented involving two masses and a pulley system. The larger mass \( M = 5 \, \text{kg} \), the smaller mass \( m = 3 \, \text{kg} \), and the kinetic frictional coefficient \( \mu_k = 0.25 \) between the surface and the larger mass \( M \). The smaller mass \( m \) is initially positioned 3 meters above the ground. **Diagram Description:** The diagram illustrates a horizontal surface where the larger mass \( M \) rests. It is connected to a smaller mass \( m \) by a rope that passes over a pulley. The rope is assumed to be massless and frictionless. The smaller mass \( m \) hangs vertically, extending 3 meters upward from the ground. **Analysis Questions:** **14. Find the work done by the friction as the larger mass \( M \) slides through a distance of 4 meters.** - **Solution Approach:** To calculate the work done by friction, use the formula: \[ \text{Work} = \text{frictional force} \times \text{distance} \] The frictional force \( = \mu_k \times M \times g \), where \( g = 9.8 \, \text{m/s}^2 \). **15. Find the speed of the smaller mass \( m \) when it touches the ground.** - **Solution Approach:** Apply the conservation of energy principle or use kinematic equations to find the speed of the smaller mass \( m \) as it descends and touches the ground. This setup can be elaborated through equations to solve these problems quantitatively, encouraging students to apply their understanding of mechanics, involving concepts such as Newton's laws, friction, and energy conservation.
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