2. A box that weighs 10.0 N is being dragged with constant velocity along a horizontal surface of the table by a rope that is at an angle ¥á of 45¨¬ with that surface. The tension in the rope is 5.0 N. What is the coefficient of friction?

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To find the coefficient of friction in this scenario, we can use the following equation:

μ = (Tension in the rope - Force due to the weight) / (Force normal to the surface)

First, let's determine the force due to the weight of the box. Weight is defined as the mass of an object multiplied by the acceleration due to gravity (9.8 m/s²). We are given that the weight of the box is 10.0 N, so we can calculate the mass of the box using the equation:

Weight = mass * acceleration due to gravity
10.0 N = mass * 9.8 m/s²

Solving for mass:
mass = 10.0 N / 9.8 m/s² = 1.02 kg

Next, we need to calculate the force normal to the surface. Since the box is on a horizontal surface, the normal force is equal in magnitude but opposite in direction to the force due to the weight of the box. Therefore, the force normal to the surface is also 10.0 N.

Now, we can substitute the given values into the equation for the coefficient of friction:

μ = (5.0 N - 10.0 N) / 10.0 N
μ = -5.0 N / 10.0 N
μ = -0.5

The negative sign indicates that the friction force is acting in the opposite direction to the motion, which is expected since the box is being dragged along the surface.

Therefore, the coefficient of friction in this case is -0.5.