How high will a winch motor with a POWER of 483 Watts lift a 18 kg crate straight up against gravity in 29 seconds. Your Answer:

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Chapter1: Units, Trigonometry. And Vectors
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**Question:**

How high will a winch motor with a power of 483 Watts lift an 18 kg crate straight up against gravity in 29 seconds?

**Your Answer:**

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*Explanation for Educational Purposes:*

To determine the height the crate will be lifted, you can use the formula for power:

\[ \text{Power (P)} = \frac{\text{Work (W)}}{\text{Time (t)}} \]

Where Work (W) is defined as:

\[ W = \text{Force (F)} \times \text{Distance (d)} \]

The force here is equal to the weight of the crate, which is mass (m) times gravity (g):

\[ F = m \times g \]

Substituting these into the power formula gives:

\[ P = \frac{m \times g \times d}{t} \]

Rearrange this to solve for distance (d):

\[ d = \frac{P \times t}{m \times g} \]

Inserting the values: 
- Power (P) = 483 Watts
- Time (t) = 29 seconds
- Mass (m) = 18 kg
- Gravity (g) = 9.81 m/s² (approximately)

\[ d = \frac{483 \times 29}{18 \times 9.81} \]

Calculate this value to find how high the crate will be lifted.
Transcribed Image Text:--- **Question:** How high will a winch motor with a power of 483 Watts lift an 18 kg crate straight up against gravity in 29 seconds? **Your Answer:** --- *Explanation for Educational Purposes:* To determine the height the crate will be lifted, you can use the formula for power: \[ \text{Power (P)} = \frac{\text{Work (W)}}{\text{Time (t)}} \] Where Work (W) is defined as: \[ W = \text{Force (F)} \times \text{Distance (d)} \] The force here is equal to the weight of the crate, which is mass (m) times gravity (g): \[ F = m \times g \] Substituting these into the power formula gives: \[ P = \frac{m \times g \times d}{t} \] Rearrange this to solve for distance (d): \[ d = \frac{P \times t}{m \times g} \] Inserting the values: - Power (P) = 483 Watts - Time (t) = 29 seconds - Mass (m) = 18 kg - Gravity (g) = 9.81 m/s² (approximately) \[ d = \frac{483 \times 29}{18 \times 9.81} \] Calculate this value to find how high the crate will be lifted.
Expert Solution
Step 1

Given data: 

Power (P) = 483 Watts

Mass (m) = 18 kg

Time (t) = 29 seconds

Required:

The height (h)

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