Question
A 6-column table with 2 rows. The first column labeled number of washers has entries 1, 3. The second column labeled Mass of Washers m subscript w (grams) has entries 4.9, 14.7. The third column labeled Mass of Washers m subscript w (kilograms) has entries 0.0049, empty. The fourth column labeled Acceleration due to Gravity a subscript g (meters per seconds squared) has entries empty, 10. The fifth column labeled Force of gravity on the washers F subscript g (kilograms times meters per second squared) has entries 0.049, 0.147. The sixth column labeled Applied force of washers on the car F subscript w c (Newtons) has entries 0049, empty.
The acceleration due to gravity for any object, including 1 washer on the string, is always assumed to be
m/s2.
The mass of 3 washers, when converted to kg, is
kg.
The applied force of 3 washers will increase the applied force on the car to
The acceleration due to gravity for any object, including 1 washer on the string, is always assumed to be
m/s2.
The mass of 3 washers, when converted to kg, is
kg.
The applied force of 3 washers will increase the applied force on the car to
Answers
GPT-4o mini
To fill in the missing information and answer your questions, let's break down the provided data and calculate the necessary values step by step.
1. **Mass of Washers in Kilograms**
- For 1 washer: 4.9 grams = 0.0049 kg (already provided)
- For 3 washers:
\[
\text{Mass in grams} = 3 \times 4.9 \, \text{grams} = 14.7 \, \text{grams}
\]
\[
\text{Mass in kg} = 14.7 \, \text{grams} \times \frac{1 \, \text{kg}}{1000 \, \text{grams}} = 0.0147 \, \text{kg}
\]
Thus, **the mass of 3 washers in kg is 0.0147 kg.**
2. **Acceleration due to Gravity**
- The acceleration due to gravity \( a_g \) is usually taken as 9.81 m/s², but in many cases, it can be simplified to approximately 10 m/s² for ease of calculation (as you have it in the table). For consistency, we will assume \( a_g = 10 \, \text{m/s}^2 \) as you have stated.
3. **Force of Gravity on the Washers**
- The force of gravity \( F_g \) acting on the mass can be calculated using the equation:
\[
F_g = m \cdot g
\]
For 3 washers (0.0147 kg):
\[
F_g = 0.0147 \, \text{kg} \times 10 \, \text{m/s}^2 = 0.147 \, \text{N}
\]
This matches the data provided in your table, confirming its correctness.
4. **Applied Force of 3 Washers on the Car**
- The applied force \( F_{wc} \) on the car for 3 washers can be calculated using the same formula:
\[
F_{wc} = 0.0147 \, \text{kg} \times 10 \, \text{m/s}^2 = 0.147 \, \text{N}
\]
If needed, the applied force can also be verified with the consistent unit conversion as follows:
- \( F_{wc} \) should be the same as the gravitational force acting on the mass; hence,
\[
F_{wc} = F_g = 0.147 \, \text{N}
\]
So the final answers are:
- The mass of 3 washers is **0.0147 kg**.
- The applied force of 3 washers will increase the applied force on the car to **0.147 N**.
1. **Mass of Washers in Kilograms**
- For 1 washer: 4.9 grams = 0.0049 kg (already provided)
- For 3 washers:
\[
\text{Mass in grams} = 3 \times 4.9 \, \text{grams} = 14.7 \, \text{grams}
\]
\[
\text{Mass in kg} = 14.7 \, \text{grams} \times \frac{1 \, \text{kg}}{1000 \, \text{grams}} = 0.0147 \, \text{kg}
\]
Thus, **the mass of 3 washers in kg is 0.0147 kg.**
2. **Acceleration due to Gravity**
- The acceleration due to gravity \( a_g \) is usually taken as 9.81 m/s², but in many cases, it can be simplified to approximately 10 m/s² for ease of calculation (as you have it in the table). For consistency, we will assume \( a_g = 10 \, \text{m/s}^2 \) as you have stated.
3. **Force of Gravity on the Washers**
- The force of gravity \( F_g \) acting on the mass can be calculated using the equation:
\[
F_g = m \cdot g
\]
For 3 washers (0.0147 kg):
\[
F_g = 0.0147 \, \text{kg} \times 10 \, \text{m/s}^2 = 0.147 \, \text{N}
\]
This matches the data provided in your table, confirming its correctness.
4. **Applied Force of 3 Washers on the Car**
- The applied force \( F_{wc} \) on the car for 3 washers can be calculated using the same formula:
\[
F_{wc} = 0.0147 \, \text{kg} \times 10 \, \text{m/s}^2 = 0.147 \, \text{N}
\]
If needed, the applied force can also be verified with the consistent unit conversion as follows:
- \( F_{wc} \) should be the same as the gravitational force acting on the mass; hence,
\[
F_{wc} = F_g = 0.147 \, \text{N}
\]
So the final answers are:
- The mass of 3 washers is **0.0147 kg**.
- The applied force of 3 washers will increase the applied force on the car to **0.147 N**.