A 1000-N crate resting on a surface is connected to a 500-N block through a frictionless pulley . Friction between the crate and surface is enough to keep the system at rest. What is the tension and friction in newtons?

To find the tension and friction in this system, we need to analyze the forces acting on each object and apply Newton's Laws of Motion.

Let's start with the crate:

1. Identify the forces acting on the crate:
- The weight (W) of the crate, which is equal to its mass (m) multiplied by the acceleration due to gravity (g).
- The normal force (N) exerted by the surface, which is equal in magnitude and opposite in direction to the weight. Since the crate is at rest, the normal force is equal to the weight of the crate.
- The force of friction (f) between the crate and the surface. This frictional force opposes the motion of the crate.

Since the crate is at rest, the sum of the horizontal forces and the sum of the vertical forces must cancel each other out. This leads to the following equations:

ΣF_horizontal = 0 : T - f = 0 (Equation 1)
ΣF_vertical = 0 : N - W = 0 (Equation 2)

Now let's move on to the 500-N block:

2. Identify the forces acting on the block:
- The weight of the block, which is equal to its mass multiplied by the acceleration due to gravity.
- The tension in the rope, which is the force transmitted through the pulley to the block.

Since the block is at rest, the vertical forces must cancel each other out:

ΣF_vertical = 0 : T - W_block = 0 (Equation 3)

From Equation 3, we can determine the tension in the rope (T):

T = W_block

Substituting this into Equation 1, we get:

W_block - f = 0

Since we know that W_block = 500 N, we can find the force of friction (f):

f = W_block = 500 N

Therefore, the tension in the rope is T = 500 N, and the force of friction is f = 500 N.