What is the force exerted by the rope on the bucket of water?

[Claudia16]

Homework Statement

a 5.9 kg bucket of water is raised from a well by a rope.
the acceleration of gravity is 9.81 m/s^2
if the upward acceleration of the bucket is 4.0 ,\m/s^2, find the force exerted by the rope on the bucket of water. in units of N

Homework Equations

The Attempt at a Solution

ok i know that i have two forces.
1. The weight of the bucket which is downward:
2. The force by the rope which should be upward in orderto overcome the weight and gives the bucket an upward acceleation

 

[PhanthomJay]

Homework Statement

a 5.9 kg bucket of water is raised from a well by a rope.
the acceleration of gravity is 9.81 m/s^2
if the upward acceleration of the bucket is 4.0 ,\m/s^2, find the force exerted by the rope on the bucket of water. in units of N

Homework Equations

The Attempt at a Solution

Welcome to PF!

ok i know that i have two forces.

yes

1. The weight of the bucket which is downward:

yes

2. The force by the rope which should be upward in orderto overcome the weight and gives the bucket an upward acceleation

yes, the upward force must be greater than the weight to produce a net upward force giving an upward acceleration. What does Newton 2 say about net forces?

 

[Claudia16]

A particle will stay at rest or continue at a constant velocity unless acted upon by an external unbalanced net force

 

[Claudia16]

F = ma: the net force on an object is equal to the mass of the object multiplied by its acceleration

 

[PhanthomJay]

F = ma: the net force on an object is equal to the mass of the object multiplied by its acceleration

OK. So find the net unbalanced force in terms of the unknown rope force (call it T) and the bucket's weight. Then set it equal to m*a to solve for T.

 

[Claudia16]

ok so the mass of the bucket (m) times the acceleration of the bucket (a) will give me T= the force exerted by the rope??

 

[hsywci]

set one direction as positive (either up or down)

then F=m(aup-adown)

 

[PhanthomJay]

ok so the mass of the bucket (m) times the acceleration of the bucket (a) will give me T= the force exerted by the rope??

No, the mass of the bucket (m) times the acceleration of the bucket (a) will give the NET force acting on the bucket. The NET force is in the upward direction (T (up) minus the bucket weight (down) = net force).