A 5.0-kg bucket of water is raised from a well by a rope. If the upward acceleration of the bucket is 3.0 m/s2, find the force exerted by the rope on the bucket.

65 N

Explanation:

ΣForces = (mass) (acceleration) = all other forces being enacted

The force that the rope exerts is just the tension in the rope caused by the bucket being lifted. I'll take up to be positive and down to be negative, so the tension is an upward force vector and the bucket weight is a downward force vector. By taking into account all the forces involved here, we get the formula:

ΣForces=ma=Tension-mg

m is the bucket mass g is gravity pulling down on the bucket, I'm also taking gravity as 10m/s² a is the upward acceleration of the bucket

By isolating Tension we get Tension=ma+mg

Tension = m (a+g)

Tension = 5kg (3+10) m/s²

Tension = (5) (13) N

Tension = 65N