Determine the weight in newtons of a car whose mass is 1400 kg. Convert the mass of the car to slugs and then determine its weight in pounds.
The Correct Answer and Explanation is :
Explanation:
To find the weight of a car with a mass of 1400 kg, we need to determine the weight in two units: Newtons (N) and pounds (lbs). The weight of an object depends on its mass and the gravitational force acting on it.
Step 1: Convert the Mass to Weight in Newtons (N)
The weight of an object is given by the formula:
[
W = m \cdot g
]
Where:
- (W) is the weight in newtons.
- (m) is the mass of the object.
- (g) is the acceleration due to gravity, which on Earth is approximately 9.81 m/s².
Given:
- Mass of the car, (m = 1400 \, \text{kg})
- Gravitational acceleration, (g = 9.81 \, \text{m/s}^2)
Substituting the values:
[
W = 1400 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 13734 \, \text{N}
]
Thus, the weight of the car in newtons is 13734 N.
Step 2: Convert the Mass to Slugs
In the imperial system, mass is often measured in slugs. To convert from kilograms to slugs, we use the following conversion factor:
[
1 \, \text{kg} = 0.0685218 \, \text{slugs}
]
So, for a car with a mass of 1400 kg:
[
\text{Mass in slugs} = 1400 \, \text{kg} \times 0.0685218 \, \text{slugs/kg} = 95.93 \, \text{slugs}
]
Thus, the car’s mass is approximately 95.93 slugs.
Step 3: Determine the Weight in Pounds
In the imperial system, weight is typically measured in pounds (lbs), and weight in pounds is related to mass in slugs by the equation:
[
W_{\text{lbs}} = m_{\text{slugs}} \times 32.174 \, \text{ft/s}^2
]
Where 32.174 ft/s² is the gravitational acceleration in the imperial system.
Substituting the values:
[
W_{\text{lbs}} = 95.93 \, \text{slugs} \times 32.174 \, \text{ft/s}^2 = 3080.63 \, \text{lbs}
]
Thus, the weight of the car is approximately 3080.63 pounds.
Final Answers:
- Weight in Newtons: 13734 N
- Mass in Slugs: 95.93 slugs
- Weight in Pounds: 3080.63 lbs
I’ll now generate an image to summarize this.
Here is the diagram showing the conversion of the car’s mass and weight. It highlights the steps involved in calculating the weight in newtons, converting the mass to slugs, and determining the weight in pounds. Let me know if you need any further explanations!