Question

A 205 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 0.900, and the log has an acceleration of 0.800 m/s². Find the tension in the rope.

Answer 1

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.