A painter in a crate which hangs alongside a building, weighs 1000N.When the painter pull on the rope, the force he exerts on the floor of the crate is 450N. If the crate wieghs 250N, find the acceleration.

but the answer given is 2?

I don't understand how to find the resultant force, who can help me?

To find the acceleration, we need to apply 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.

First, let's calculate the net force acting on the crate. The weight of the crate is given as 250N, and the force exerted by the painter on the floor of the crate is 450N. Since these forces act in opposite directions, we subtract the force exerted by the painter from the weight of the crate:

Net force = Weight of the crate - Force exerted by the painter
Net force = 250N - 450N
Net force = -200N

Note that the negative sign indicates that the forces have opposite directions.

Now, we can use Newton's second law to find the acceleration. Since the net force is equal to the mass of the object multiplied by its acceleration, we can rearrange the equation to solve for acceleration:

Net force = mass × acceleration

Since the mass of the crate is not given explicitly, we can calculate it by dividing its weight by the acceleration due to gravity, which is approximately 9.8 m/s^2:

mass = weight / acceleration due to gravity
mass = 250N / 9.8 m/s^2
mass ≈ 25.51 kg (rounded to two decimal places)

Now we can substitute the values for the net force and mass into the equation to solve for acceleration:

-200N = 25.51 kg × acceleration

To isolate acceleration, we need to divide both sides of the equation by the mass:

acceleration = -200N / 25.51 kg
acceleration ≈ -7.83 m/s^2 (rounded to two decimal places)

Therefore, the acceleration of the crate is approximately -7.83 m/s^2. The negative sign indicates that the crate is accelerating in the opposite direction of the net force.

There is an upward force of 500 N on the crate plus painter, due to both ends of the rope he is pulling. There is a downward gravity force of 450 N, resulting in a net force of 50N up.

a = Fnet/Mtotal = 50/(1250/g)= g/25