One slug is equivalent to 14.6kg
. A force of 10 pound is applied on a body of one
. The acceleration of the body is: (a) 44.5 m/s
(b) 4.448M/S
(c ) 44.4fts
(d) none of these
To solve this problem, we need to apply Newton’s second law of motion, which states that: F=maF = maF=ma
where:
- FFF is the force,
- mmm is the mass,
- aaa is the acceleration.
We are given:
- The force F=10 poundsF = 10 \, \text{pounds}F=10pounds,
- The mass of the body m=1 slugm = 1 \, \text{slug}m=1slug,
- The relationship between slugs and kilograms: 1 slug=14.6 kg1 \, \text{slug} = 14.6 \, \text{kg}1slug=14.6kg.
Step 1: Convert the force from pounds to Newtons
To use the metric system in SI units (meters, kilograms, seconds), we need to convert pounds into Newtons. The conversion factor is: 1 pound=4.448 Newtons1 \, \text{pound} = 4.448 \, \text{Newtons}1pound=4.448Newtons
Thus, the force in Newtons is: F=10 pounds×4.448 N/pound=44.48 NewtonsF = 10 \, \text{pounds} \times 4.448 \, \text{N/pound} = 44.48 \, \text{Newtons}F=10pounds×4.448N/pound=44.48Newtons
Step 2: Convert mass from slugs to kilograms
Since we know that 1 slug=14.6 kg1 \, \text{slug} = 14.6 \, \text{kg}1slug=14.6kg, the mass of the body in kilograms is: m=1 slug×14.6 kg/slug=14.6 kgm = 1 \, \text{slug} \times 14.6 \, \text{kg/slug} = 14.6 \, \text{kg}m=1slug×14.6kg/slug=14.6kg
Step 3: Calculate the acceleration
Now we can use Newton’s second law to calculate the acceleration: a=Fma = \frac{F}{m}a=mF
Substituting the values for force and mass: a=44.48 N14.6 kg=3.05 m/s2a = \frac{44.48 \, \text{N}}{14.6 \, \text{kg}} = 3.05 \, \text{m/s}^2a=14.6kg44.48N=3.05m/s2
Conclusion:
The acceleration of the body is approximately 3.05 m/s23.05 \, \text{m/s}^23.05m/s2, which is not listed as one of the answer choices. Therefore, the correct answer is (d) none of these.
