A 5.2 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.
Answer in units of N.

To find the force exerted by the rope on the bucket of water, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).

Given:
Mass of the bucket of water (m) = 5.2 kg
Acceleration due to gravity (g) = 9.81 m/s^2
Upward acceleration of the bucket (a) = 4.0 m/s^2

First, we need to find the net force acting on the bucket. The net force is the sum of the gravitational force (mg) and the force exerted by the rope (F_rope).

Using Newton's second law, we can write the equations:
F_net = F_rope - mg
F_net = ma

Since the bucket is being raised upward, the net force should be in the upward direction.

The gravitational force on the bucket is given by:
mg = (mass)(acceleration due to gravity)
mg = (5.2 kg)(9.81 m/s^2)

Substituting the known values, we have:
mg = 50.892 kg∙m/s^2

Now, we can substitute the values into the equation F_net = ma:
F_rope - mg = ma

Rearranging the equation to solve for the force exerted by the rope:
F_rope = ma + mg

Substituting the known values, we have:
F_rope = (5.2 kg)(4.0 m/s^2) + 50.892 kg∙m/s^2

Calculating the values, we get:
F_rope = 20.8 kg∙m/s^2 + 50.892 kg∙m/s^2

Combining the terms, we get:
F_rope = 71.692 kg∙m/s^2

Finally, we can convert kg∙m/s^2 to Newtons (N) by using the conversion factor 1 N = 1 kg∙m/s^2.

Therefore, the force exerted by the rope on the bucket of water is approximately 71.692 Newtons (N).

To find the force exerted by the rope on the bucket of water, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

In this case, the mass of the bucket of water is given as 5.2 kg, and the upward acceleration of the bucket is 4.0 m/s^2.

The force exerted by the rope on the bucket can be calculated using the formula:

Force = mass x acceleration

Substituting the given values, we get:

Force = 5.2 kg x 4.0 m/s^2

Now, we can simply multiply the values to find the force exerted by the rope on the bucket:

Force = 20.8 N

Therefore, the force exerted by the rope on the bucket of water is 20.8 Newtons (N).

F up

m g down

F = m a
Fup - m g = m a
so
Fup = m (g+a)

= 5.2 (9.81 + 4) Newtons