A 4.3 kg bucket of water is raised from a well
by a rope.
The acceleration of gravity is 9.8 m/s2 .
If the upward acceleration of the bucket is
4.6 m/s2, find the force exerted by the rope
on the bucket.
Answer in units of N.
I'm almost sure the answer requires me to use Fnet= F1 + F2 = ma. I still haven't figured out exactly how to do this...I keep getting the wrong answer.
tension in rope= mg+ma
To solve this problem, you can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass times its acceleration (F = m*a).
First, let's define the forces acting on the bucket:
1. The force of gravity pulling the bucket downward with a force of Fgravity = m * g, where m is the mass of the bucket and g is the acceleration due to gravity.
2. The force exerted by the rope on the bucket, which is directed upward.
According to the problem, the upward acceleration of the bucket is given as 4.6 m/s². The net force acting on the bucket is the difference between the force exerted by the rope and the force of gravity:
Fnet = Force exerted by the rope - Force of gravity
Since the force of gravity and the acceleration due to gravity point in opposite directions, we have:
Fgravity = -m * g
Substituting this into the equation for net force gives:
Fnet = Force exerted by the rope - (-m * g)
= Force exerted by the rope + m * g
Now, we can substitute the given values into the equation:
m = 4.3 kg (mass of the bucket)
g = 9.8 m/s² (acceleration due to gravity)
Fnet = Force exerted by the rope + (4.3 kg) * (9.8 m/s²)
We are given that the upward acceleration of the bucket is 4.6 m/s². Since the net force is equal to mass times acceleration, we have:
Fnet = (4.3 kg) * (4.6 m/s²)
Now, calculate the value of Fnet:
Fnet = 19.78 N
Hence, the force exerted by the rope on the bucket is approximately 19.78 Newtons.