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**Question 4** A child does 350 J of work while pulling a box from the ground up to his tree house with a rope. The tree house is 9.0 m above the ground. What is the mass of the box? - [ ] 4.0 kg - [ ] 3.6 kg - [ ] 2.4 kg - [ ] 3.0 kg --- **Explanation:** The problem involves finding the mass of a box based on the work done to lift it and the height it was lifted. Given the work-energy principle and gravitational potential energy, we can solve this by using the relationship: \[ \text{Work Done (W)} = \text{Gravitational Potential Energy (U)} = m \cdot g \cdot h \] Where: - \( W \) is the work done (350 J) - \( m \) is the mass of the box (in kg) - \( g \) is the acceleration due to gravity (\( \approx 9.8 \, \text{m/s}^2 \)) - \( h \) is the height (9.0 m) Rearranging the formula to solve for \( m \): \[ m = \frac{W}{g \cdot h} \] Substitute the known values: \[ m = \frac{350}{9.8 \cdot 9.0} \] \[ m = \frac{350}{88.2} \] \[ m = 3.97 \, \text{kg} \] Thus, the nearest mass from the given multiple-choice options is **4.0 kg**.

**Question 4** A child does 350 J of work while pulling a box from the ground up to his tree house with a rope. The tree house is 9.0 m above the ground. What is the mass of the box? - [ ] 4.0 kg - [ ] 3.6 kg - [ ] 2.4 kg - [ ] 3.0 kg --- **Explanation:** The problem involves finding the mass of a box based on the work done to lift it and the height it was lifted. Given the work-energy principle and gravitational potential energy, we can solve this by using the relationship: \[ \text{Work Done (W)} = \text{Gravitational Potential Energy (U)} = m \cdot g \cdot h \] Where: - \( W \) is the work done (350 J) - \( m \) is the mass of the box (in kg) - \( g \) is the acceleration due to gravity (\( \approx 9.8 \, \text{m/s}^2 \)) - \( h \) is the height (9.0 m) Rearranging the formula to solve for \( m \): \[ m = \frac{W}{g \cdot h} \] Substitute the known values: \[ m = \frac{350}{9.8 \cdot 9.0} \] \[ m = \frac{350}{88.2} \] \[ m = 3.97 \, \text{kg} \] Thus, the nearest mass from the given multiple-choice options is **4.0 kg**.

College Physics
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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**Question 4** A child does 350 J of work while pulling a box from the ground up to his tree house with a rope. The tree house is 9.0 m above the ground. What is the mass of the box? - [ ] 4.0 kg - [ ] 3.6 kg - [ ] 2.4 kg - [ ] 3.0 kg --- **Explanation:** The problem involves finding the mass of a box based on the work done to lift it and the height it was lifted. Given the work-energy principle and gravitational potential energy, we can solve this by using the relationship: \[ \text{Work Done (W)} = \text{Gravitational Potential Energy (U)} = m \cdot g \cdot h \] Where: - \( W \) is the work done (350 J) - \( m \) is the mass of the box (in kg) - \( g \) is the acceleration due to gravity (\( \approx 9.8 \, \text{m/s}^2 \)) - \( h \) is the height (9.0 m) Rearranging the formula to solve for \( m \): \[ m = \frac{W}{g \cdot h} \] Substitute the known values: \[ m = \frac{350}{9.8 \cdot 9.0} \] \[ m = \frac{350}{88.2} \] \[ m = 3.97 \, \text{kg} \] Thus, the nearest mass from the given multiple-choice options is **4.0 kg**.
Transcribed Image Text:**Question 4** A child does 350 J of work while pulling a box from the ground up to his tree house with a rope. The tree house is 9.0 m above the ground. What is the mass of the box? - [ ] 4.0 kg - [ ] 3.6 kg - [ ] 2.4 kg - [ ] 3.0 kg --- **Explanation:** The problem involves finding the mass of a box based on the work done to lift it and the height it was lifted. Given the work-energy principle and gravitational potential energy, we can solve this by using the relationship: \[ \text{Work Done (W)} = \text{Gravitational Potential Energy (U)} = m \cdot g \cdot h \] Where: - \( W \) is the work done (350 J) - \( m \) is the mass of the box (in kg) - \( g \) is the acceleration due to gravity (\( \approx 9.8 \, \text{m/s}^2 \)) - \( h \) is the height (9.0 m) Rearranging the formula to solve for \( m \): \[ m = \frac{W}{g \cdot h} \] Substitute the known values: \[ m = \frac{350}{9.8 \cdot 9.0} \] \[ m = \frac{350}{88.2} \] \[ m = 3.97 \, \text{kg} \] Thus, the nearest mass from the given multiple-choice options is **4.0 kg**.
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