### Physics Problem: Calculating the Speed of a Car#### Problem Statement**Question 18:** What is the speed of an 800-kg car whose kinetic energy (KE) is 250 kJ?#### Detailed ExplanationTo solve this problem, we need to use the formula for kinetic energy: \[ KE = \frac{1}{2}mv^2 \]Where:- \( KE \) is the kinetic energy- \( m \) is the mass of the object- \( v \) is the velocity (or speed) of the objectGiven:- \( KE = 250 \text{kJ} = 250,000 \text{J} \)- \( m = 800 \text{kg} \)We need to find the speed \( v \).#### Step-by-Step Solution1. **Start with the kinetic energy formula:**\[ KE = \frac{1}{2}mv^2 \]2. **Rearrange the formula to solve for \( v \):**\[ v^2 = \frac{2 \cdot KE}{m} \]\[ v = \sqrt{\frac{2 \cdot KE}{m}} \]3. **Substitute the given values into the formula:**\[ v = \sqrt{\frac{2 \cdot 250,000}{800}} \]4. **Calculate the values step-by-step:**\[ v = \sqrt{\frac{500,000}{800}} \]\[ v = \sqrt{625} \]\[ v = 25 \text{ m/s} \]#### Final AnswerThe speed of the 800-kg car with a kinetic energy of 250 kJ is **25 meters per second (m/s)**. **Problem 13****Question:**A 700-kg horse, whose power output is 1.0 hp, is pulling a sled over the snow at 3.5 m/s. Find the force the horse exerts on the sled.---**Explanation:**This problem involves calculating the force exerted by a horse while pulling a sled, given the horse's power output and the sled’s velocity. The relevant concepts include the relationship between power, force, and velocity.---**Solution:**1. **Given Data:** - Mass of the horse (\( m \)) = 700 kg - Power output (\( P \)) = 1.0 hp (horsepower) - Speed of the sled (\( v \)) = 3.5 m/s2. **Conversion of Units:** - 1 horsepower (hp) is equivalent to 745.7 watts (W). Thus, power in watts: \[ P = 1.0 \, \text{hp} \times 745.7 \, \frac{\text{W}}{\text{hp}} = 745.7 \, \text{W} \]3. **Power Equation:** The formula to relate power, force, and velocity is given by: \[ P = F \times v \] Where: - \( P \) is the power, - \( F \) is the force, - \( v \) is the velocity.4. **Calculate Force:** Rearrange the equation to solve for force (\( F \)): \[ F = \frac{P}{v} \] Plug in the given values: \[ F = \frac{745.7 \, \text{W}}{3.5 \, \text{m/s}} \approx 213 \, \text{N} \]**Answer:**The force the horse exerts on the sled is approximately 213 Newtons (N).---This solution incorporates the necessary steps to convert units, use the appropriate formula, and calculate the required force, making it suitable for educational purposes.

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Answered: 13. A 700-kg horse whose power output…

13. A 700-kg horse whose power output is 1.0 hp is pulling a sled over the snow at 3.5 m/s. Find the force the horse exerts on the sled.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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