A 260-kg log is pulled up a ramp by means of a rope that is parallel to the surface of the ramp. The ramp is inclined at 30.0° with respect to the horizontal. The coefficient of kinetic friction between the log and the ramp is 0.870, and the log has an acceleration of 0.800 m/s2. Find the tension in the rope.
To find the tension in the rope, we can use Newton's second law and resolve the forces acting on the log.
The formula to calculate the tension in the rope is:
Tension = (mass of the log) × (acceleration of the log) + (force of friction)
First, let's find the force of friction. The formula to calculate the force of friction is:
Force of friction = (coefficient of friction) × (normal force)
where the normal force is the force perpendicular to the surface. In this case, it is equal to the weight of the log.
The formula to calculate the weight of an object is:
Weight = (mass of the object) × (acceleration due to gravity)
Given values:
Mass of the log = 260 kg
Acceleration due to gravity = 9.8 m/s² (approximate value)
Coefficient of kinetic friction = 0.870
Angle of the ramp = 30°
Weight = (260 kg) × (9.8 m/s²)
Weight ≈ 2548 N
Normal force = Weight × cos(angle of the ramp)
Normal force ≈ 2548 N × cos(30°)
Now, let's calculate the force of friction:
Force of friction = (0.870) × (normal force)
Next, we can calculate the tension in the rope using Newton's second law:
Tension = (mass of the log) × (acceleration of the log) + (force of friction)
Finally, substitute the known values into the equation and solve for tension.