Sure, let's solve this step by step.

Step 1: Identify the forces acting on the block.
There are three forces acting on the block:
- The weight of the block (W = m*g), which acts vertically downwards.
- The normal force (N), which acts perpendicular to the slope.
- The frictional force (F), which acts parallel to the slope and opposes the motion of the block.

Step 2: Resolve the weight of the block into components.
The weight of the block can be resolved into two components: one acting perpendicular to the slope (Wcosθ) and one acting parallel to the slope (Wsinθ). Here, θ is the angle of the slope.

Step 3: Apply Newton's second law.
According to Newton's second law, the net force acting on the block is equal to the mass of the block times its acceleration. The net force acting on the block is the difference between the component of the weight acting parallel to the slope and the frictional force. So, we have:

m*a = Wsinθ - F

Step 4: Express the frictional force in terms of the coefficient of dynamic friction.
The frictional force can be expressed as the product of the coefficient of dynamic friction (μd) and the normal force. The normal force is equal to the component of the weight acting perpendicular to the slope. So, we have:

F = μd * N = μd * Wcosθ

Step 5: Substitute the expressions for the frictional force and the component of the weight acting parallel to the slope into the equation from step 3 and solve for μd.
We get:

m*a = m*g*sinθ - μd * m*g*cosθ

Rearranging for μd gives:

μd = (m*g*sinθ - m*a) / (m*g*cosθ)

Step 6: Substitute the given values into the equation from step 5 and solve for μd.
Given: m = 2.80 kg, g = 9.81 m/s², a = 0.360 m/s², and θ = 16.0°, we get:

μd = ((2.80 kg * 9.81 m/s² * sin(16.0°)) - (2.80 kg * 0.360 m/s²)) / (2.80 kg * 9.81 m/s² * cos(16.0°))

Solving this gives the coefficient of dynamic friction.

Question

Sure, let's solve this step by step.

Step 1: Identify the forces acting on the block.
There are three forces acting on the block: 
- The weight of the block (W = m*g), which acts vertically downwards.
- The normal force (N), which acts perpendicular to the slope.
- The frictional force (F), which acts parallel to the slope and opposes the motion of the block.

Step 2: Resolve the weight of the block into components.
The weight of the block can be resolved into two components: one acting perpendicular to the slope (Wcosθ) and one acting parallel to the slope (Wsinθ). Here, θ is the angle of the slope.

Step 3: Apply Newton's second law.
According to Newton's second law, the net force acting on the block is equal to the mass of the block times its acceleration. The net force acting on the block is the difference between the component of the weight acting parallel to the slope and the frictional force. So, we have:

m*a = Wsinθ - F

Step 4: Express the frictional force in terms of the coefficient of dynamic friction.
The frictional force can be expressed as the product of the coefficient of dynamic friction (μd) and the normal force. The normal force is equal to the component of the weight acting perpendicular to the slope. So, we have:

F = μd * N = μd * Wcosθ

Step 5: Substitute the expressions for the frictional force and the component of the weight acting parallel to the slope into the equation from step 3 and solve for μd.
We get:

m*a = m*g*sinθ - μd * m*g*cosθ

Rearranging for μd gives:

μd = (m*g*sinθ - m*a) / (m*g*cosθ)

Step 6: Substitute the given values into the equation from step 5 and solve for μd.
Given: m = 2.80 kg, g = 9.81 m/s², a = 0.360 m/s², and θ = 16.0°, we get:

μd = ((2.80 kg * 9.81 m/s² * sin(16.0°)) - (2.80 kg * 0.360 m/s²)) / (2.80 kg * 9.81 m/s² * cos(16.0°))

Solving this gives the coefficient of dynamic friction.

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