A 239-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 29.0° with respect to the horizontal. The coefficient of kinetic friction between the log and the ramp is 0.800, and the log has an acceleration of 0.900 m/s2. Find the tension in the rope.

Question

A 239-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 29.0° with respect to the horizontal. The coefficient of kinetic friction between the log and the ramp is 0.800, and the log has an acceleration of 0.900 m/s2. Find the tension in the rope.

Answer 1

Net force up=mass*acceleration

Now net force up=pulling force - friction-weightdireceddownslop
=pulling force-mg*mu*cosTheta -mgSinTheta

Answer 2

Sue and Jenny kick a soccer ball at exactly force of 85.4 N to the east.

Answer 3

To find the tension in the rope, we need to analyze the forces acting on the log.

First, let's break down the forces acting on the log:

1. The force of gravity (weight): This force acts vertically downwards and can be calculated using the equation: weight = mass * gravitational acceleration (W = m*g), where mass (m) of the log is given as 239 kg, and the gravitational acceleration (g) is approximately 9.8 m/s^2.

So, weight = 239 kg * 9.8 m/s^2 = 2342.2 N.

2. The normal force: This force acts perpendicular to the ramp and is equal in magnitude but opposite in direction to the vertical component of the weight. On an inclined plane, the normal force can be calculated using the equation: normal force = weight * cosine(angle of incline).

So, normal force = 2342.2 N * cos(29°).

3. The force of friction: This force opposes the motion of the log and can be calculated using the equation: force of friction = coefficient of friction * normal force.

So, force of friction = 0.800 * normal force.

Now, let's calculate the net force acting on the log:

Net force = force applied - force of friction.

The force applied is the tension in the rope.

Since the log has an acceleration of 0.900 m/s^2, we can calculate the net force using the equation: net force = mass * acceleration.

So, net force = 239 kg * 0.900 m/s^2.

Now, setting the net force equal to the force applied minus the force of friction:

Net force = T - force of friction.

Substituting the known values, we have:

239 kg * 0.900 m/s^2 = T - 0.800 * normal force.

To solve for T, we need to find the value of the normal force:

normal force = weight * cosine(angle of incline) = 2342.2 N * cos(29°).

Next, plug in this value of the normal force into the equation above and solve for T, which will give us the tension in the rope.