To determine the force required to move a body vertically upward with a given acceleration, we need to consider the net force acting on the body. In this case, the net force will be the sum of the force required to counteract the body's weight and the force required to produce the desired acceleration.
The weight of the body is given as 20N, which is the force due to gravity acting vertically downward. Since we want to move the body vertically upward, we need to counteract this force.
To calculate the force required to counteract the weight, we use Newton's second law of motion:
Force = mass × acceleration
In this case, the acceleration is the opposite of the desired acceleration (negative because we want to move upward), so it will be -2m/s².
Let's assume the body's mass is represented by "m." Then, we have:
20N = m × (-2m/s²)
Simplifying the equation, we find:
-2m²/s² = 20N
To solve for "m," we can rearrange the equation as follows:
m² = -20N/(-2m/s²)
m² = 10kg
Taking the square root of both sides, we find:
m ≈ √10 ≈ 3.16kg
Now that we know the mass of the body is approximately 3.16kg, we can calculate the force required to move it upward with the given acceleration:
Force = mass × acceleration Force = 3.16kg × (-2m/s²) Force ≈ -6.32N
Therefore, approximately 6.32 Newtons of force are required to move the body vertically upward with an acceleration of 2m/s². The negative sign indicates that the force is acting in the opposite direction of the desired motion.