Find The Value Of 15.0 n In Pounds. Use The Conversions 1slug=14.59kg And 1ft=0.3048m

To find the value of 15.0 n (newtons) in pounds, we need to use the given conversions and follow these steps:

Step 1: Understand the Problem

• You are given 15.0 newtons (N) and need to convert this force into pounds (lb).
• The conversion factors provided are:
  • 1 slug = 14.59 kg
  • 1 ft = 0.3048 m

Step 2: Convert Newtons to Pounds

1. Convert Newtons to Kilograms:

   • 1 Newton (N) is equal to 1 kg·m/s².
   • However, to convert force from newtons to pounds, we need to consider the relationship between mass, acceleration, and force.

2. Use the gravitational force equation:

   • The gravitational force on Earth is approximately 9.81 m/s².
   • Weight (force) in newtons is mass (in kg) multiplied by acceleration due to gravity.
   • To convert newtons to pounds, we’ll use the following relationship: 1 lb=1 slug×32.2 ft/s2\text{1 lb} = \text{1 slug} \times \text{32.2 ft/s}^21 lb=1 slug×32.2 ft/s2
   • Convert the weight in newtons to slugs and then to pounds.

Step 3: Perform the Conversion

1. Convert Newtons to slugs:

   • Given that 1 slug = 14.59 kg and 1 ft = 0.3048 m, we can use the fact that: 1 N=19.81 kg\cdotpm/s21 \text{ N} = \frac{1}{9.81} \text{ kg·m/s}^21 N=9.811​ kg\cdotpm/s2 And since 1 slug is equivalent to 32.2 lb (because 1 slug=1 lb⋅32.2 ft/s21\text{1 slug} = 1 \text{ lb}\cdot \frac{\text{32.2 ft/s}^2}{1}1 slug=1 lb⋅132.2 ft/s2​): 1 N=19.81×1 lb\text{1 N} = \frac{1}{9.81} \times \text{1 lb}1 N=9.811​×1 lb

2. Convert 15.0 N to Pounds:

15.0 N×1 lb4.44822 N≈3.37 lb\text{15.0 N} \times \frac{1 \text{ lb}}{4.44822 \text{ N}} \approx \text{3.37 lb}15.0 N×4.44822 N1 lb​≈3.37 lb

So, the value of 15.0 newtons is approximately 3.37 pounds.