Final answer:
To find the tension in the rope, calculate the forces of gravity and friction, and use the net force equation. Then substitute the known values to find the tension.
Step-by-step explanation:
To find the tension in the rope, we need to analyze the forces acting on the log. There are two main forces: the force of gravity and the force of friction. Both forces are opposed to the motion of the log.
Step 1: Calculate the force of gravity using the formula:
Fgravity = m * g
where m is the mass of the log and g is the acceleration due to gravity (approximately 9.8 m/s²).
Step 2: Calculate the force of friction using the formula:
Ffriction = μ * FN
where μ is the coefficient of friction and FN is the normal force. The normal force is equal to the component of the force of gravity perpendicular to the ramp surface.
Step 3: Calculate the net force acting on the log using the equation:
Fnet = m * a
where a is the acceleration of the log.
Step 4: Use the net force to calculate the tension in the rope using the equation:
Tension = Fnet + Ffriction
By substituting the known values into the equations, you can find the tension in the rope.