one slug is equivalent to 14.6kg. A force of 10 pound is applied on a body of 1 kg. the acceleration of the body is?
The Correct Answer and Explanation is:
To find the acceleration of the body, we need to use Newton’s Second Law of Motion, which states that the force applied on an object is equal to the product of the mass of the object and its acceleration: F=maF = maF=ma
Where:
- FFF is the force applied on the body (in Newtons, N),
- mmm is the mass of the object (in kilograms, kg),
- aaa is the acceleration (in meters per second squared, m/s²).
Step 1: Convert the Force to Newtons
The force is given as 10 pounds. To use it in the formula, we must convert pounds to Newtons because the SI unit of force is Newtons. The conversion factor from pounds to Newtons is: 1 pound=4.44822 N1 \text{ pound} = 4.44822 \text{ N}1 pound=4.44822 N
So, the force FFF in Newtons is: F=10×4.44822=44.4822 NF = 10 \times 4.44822 = 44.4822 \, \text{N}F=10×4.44822=44.4822N
Step 2: Apply Newton’s Second Law
Now that we have the force in Newtons, we can calculate the acceleration. The mass of the body is 1 kg, so we substitute the values into Newton’s second law equation: F=maF = maF=ma 44.4822 N=1 kg×a44.4822 \, \text{N} = 1 \, \text{kg} \times a44.4822N=1kg×a
Solving for aaa: a=44.4822 N1 kg=44.4822 m/s2a = \frac{44.4822 \, \text{N}}{1 \, \text{kg}} = 44.4822 \, \text{m/s}^2a=1kg44.4822N=44.4822m/s2
Final Answer
The acceleration of the body is approximately 44.48 m/s².
Explanation
The key here is converting the force from pounds to Newtons and applying Newton’s Second Law to find acceleration. The mass of the body remains constant at 1 kg, and the force applied is relatively large (44.48 N), resulting in a significant acceleration. This calculation shows how force directly influences the rate at which an object accelerates based on its mass. The greater the force, the higher the acceleration, provided the mass stays the same.
