• Children in a tree house lift a small dog in a basket 4.70 m up to their house. If it takes 201 J of work to do this, what is the combined mass of the dog and basket?

College Physics
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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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**Physics Problem: Calculating Mass from Work Done**

In this problem, children in a tree house lift a small dog in a basket to a height of 4.70 meters. The work done in lifting the basket and dog is 201 Joules. The task is to determine the combined mass of the dog and basket.

**Key Concepts:**

- **Work (W)** is the energy transferred when a force is applied over a distance. It can be calculated using the formula:
  \[
  W = F \times d
  \]
  where \(W\) is the work done (in Joules), \(F\) is the force applied (in Newtons), and \(d\) is the distance moved in the direction of the force (in meters).

- **Gravitational Force (F)** on an object is the force due to gravity:
  \[
  F = m \times g
  \]
  where \(m\) is the mass (in kilograms) and \(g\) is the acceleration due to gravity (approximately \(9.8 \, \text{m/s}^2\) on Earth).

**Solution:**

1. Use the formula for work to find the force:
   \[
   W = m \times g \times d
   \]
   Rearranging for mass (\(m\)):
   \[
   m = \frac{W}{g \times d}
   \]

2. Substitute the given values:
   \[
   m = \frac{201 \, \text{J}}{9.8 \, \text{m/s}^2 \times 4.70 \, \text{m}}
   \]

3. Calculate \(m\) to find the combined mass of the dog and basket.
Transcribed Image Text:**Physics Problem: Calculating Mass from Work Done** In this problem, children in a tree house lift a small dog in a basket to a height of 4.70 meters. The work done in lifting the basket and dog is 201 Joules. The task is to determine the combined mass of the dog and basket. **Key Concepts:** - **Work (W)** is the energy transferred when a force is applied over a distance. It can be calculated using the formula: \[ W = F \times d \] where \(W\) is the work done (in Joules), \(F\) is the force applied (in Newtons), and \(d\) is the distance moved in the direction of the force (in meters). - **Gravitational Force (F)** on an object is the force due to gravity: \[ F = m \times g \] where \(m\) is the mass (in kilograms) and \(g\) is the acceleration due to gravity (approximately \(9.8 \, \text{m/s}^2\) on Earth). **Solution:** 1. Use the formula for work to find the force: \[ W = m \times g \times d \] Rearranging for mass (\(m\)): \[ m = \frac{W}{g \times d} \] 2. Substitute the given values: \[ m = \frac{201 \, \text{J}}{9.8 \, \text{m/s}^2 \times 4.70 \, \text{m}} \] 3. Calculate \(m\) to find the combined mass of the dog and basket.
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