Answer :
The acceleration of a 10-kg mass with a rope tension of 118 N is 2 m/s², as calculated using Newton's second law by subtracting the weight of the mass from the rope tension and dividing by the mass.
To determine the acceleration of a 10-kg mass in motion with a rope tension of 118 N, we use Newton's second law, which states that the net force (Fnet) is equal to the mass (m) times its acceleration (a), or Fnet = m × a. As tension in the rope and gravity are the only forces acting on the mass, Fnet equals tension minus the gravitational force (weight), which is calculated as m × g, where g is the acceleration due to gravity (9.8 m/s²).
First, let's calculate the weight of the mass: W = m × g = 10 kg × 9.8 m/s² = 98 N.
Now, by applying Newton's second law, let's find the net force: Fnet = Tension - Weight = 118 N - 98 N = 20 N.
Finally, to find the acceleration, we rearrange the equation Fnet = m × a to solve for a: a = Fnet / m = 20 N / 10 kg = 2 m/s².
So, the acceleration of the mass is 2 m/s².
There are two forces on the mass:
-- the force of gravity downward ... (10kg) x (9.8 m/s²) = 98 newtons downward
-- the tension in the rope upward ... 118 newtons upward
The NET force on the mass is (118 - 98) = 20 newtons upward .
F = M a
Divide each side by 'M' : a = F / M
a = (20 newtons upward) / (10kg)
a = 2 m/s² upward
