https://file.aiquickdraw.com/mathbot/file/1729858279830q3hu8haq.jpg

Lee muy bien el problema y resuelve solo la pregunta c, nesesito que se analice bien y que quede correcta

Let's carefully analyze the problem and solve question **c)**, which asks for the **energy lost by the system when the truck finally comes to a stop**.

### Problem context:
1. **Initial conditions**: The truck, with a mass \( m \), descends an icy slope with no friction. The slope has an angle \( \alpha \) and the truck starts with an initial velocity \( v_0 \). The truck travels a distance \( L \) down the slope.
   
2. **Ramp conditions**: After reaching the bottom, the truck enters a safety ramp with an incline of angle \( \beta \) and this ramp has a **rolling friction** with coefficient \( \mu_k \).

3. **Objective for part c**: We need to determine the **energy lost** as the truck comes to rest. This corresponds to the **non-conservative work** done by friction and gravity as the truck moves up the safety ramp.

### Analysis for question **c)** (Energy lost):

The energy lost by the truck is the **mechanical energy** initially present minus the final mechanical energy (which is zero, since the truck stops). Here's how to approach the solution:

#### 1. **Initial Mechanical Energy (at the bottom of the slope)**:
When the truck reaches the bottom of the slope, its energy is purely **kinetic** (since potential energy is zero at the bottom). The initial kinetic energy is:

\[
E_{\text{kin}} = \frac{1}{2} m v^2
\]

where \( v \) is the velocity of the truck at the bottom, which can be found from the energy conservation equation during its descent on the icy slope.

#### 2. **Final Energy (at the top of the safety ramp)**:
At the top of the ramp, when the truck stops, all its kinetic energy has been dissipated due to friction. Thus, the final kinetic energy is **zero**.

#### 3. **Energy Lost**:
The energy lost is the total energy dissipated by friction as the truck goes up the ramp. This energy loss is equal to the **work done by friction**:

\[
W_{\text{fric}} = \text{Energy lost} = E_{\text{kin}} 
\]

Thus, the energy lost corresponds to the entire initial kinetic energy the truck had at the bottom of the slope.

### Conclusion:
The energy lost by the system when the truck comes to rest is the kinetic energy that it had at the bottom of the slope. This energy has been dissipated by the frictional force as the truck ascends the safety ramp.

\[
\boxed{E_{\text{lost}} = \frac{1}{2} m v^2}
\]

This formula expresses the energy lost when the truck comes to a stop.

Would you like further details on this or clarifications? Here are five related questions you might find useful:

1. How do we calculate the velocity at the bottom of the slope considering the height difference and angle \( \alpha \)?
2. How does the coefficient of friction \( \mu_k \) affect the stopping distance on the safety ramp?
3. What is the total distance the truck travels on the safety ramp before stopping?
4. How do you compute the work done by non-conservative forces such as friction?
5. What are the differences between conservative and non-conservative forces in energy dissipation?

**Tip**: Always remember that energy conservation is key in problems involving mechanical energy, especially when non-conservative forces like friction are present.

Lee muy bien el problema y resuelve solo la pregunta c, nesesito que se analice bien y que quede correcta.

This problem explores how to calculate the energy lost due to friction when a truck descends an icy slope and comes to a stop on a safety ramp. It involves principles of energy conservation, non-conservative work, and friction. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation