A sled loaded with bricks has a total mass of 18.0 kg and is pulled at constant speed by a rope inclined at 30.0o above the horizontal. The sledge moves a distance of 16.0 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.260 .

(a) What is the tension in the rope?

Well, if I were a sled loaded with bricks, I would probably say, "Hey there, rope! Can you please lighten the load a bit? I'm feeling a little weighed down here!" But I digress.

To find the tension in the rope, we can start by analyzing the forces acting on the sled. First, we have the weight of the sled (mg), which acts vertically downwards. We can break this force into two components: one perpendicular to the surface (mgcosθ), and one parallel to the surface (mgsinθ).

Next, we have the force of friction (Ffriction), which opposes the motion and acts parallel to the surface. We can find this force by multiplying the coefficient of kinetic friction (μk) by the perpendicular force. So, Ffriction = μk * (mgcosθ).

Since the sled is moving at a constant speed, the net force acting on it must be zero. Therefore, the tension in the rope (T) must balance out the force of friction, so T = Ffriction.

Calculating the values:
m = 18.0 kg (mass of the sled)
g = 9.8 m/s^2 (acceleration due to gravity)
θ = 30.0 degrees (angle of the rope with the horizontal)
μk = 0.260 (coefficient of kinetic friction)

Plugging these values into the equations:
Ffriction = μk * (mgcosθ) = 0.260 * (18.0 kg * 9.8 m/s^2 * cos(30.0 degrees))

Now, we can calculate the tension in the rope:
T = Ffriction

And there you have it! Use those values in the calculations and you'll find the tension in the rope. Good luck, and remember, don't go sledding without a good punchline!

To find the tension in the rope, we can start by analyzing the forces acting on the sled.

1. Gravity: The force of gravity acts vertically downward and it can be calculated using the formula Fg = m * g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2). In this case, the mass of the sled is given as 18.0 kg, so the force of gravity would be Fg = 18.0 kg * 9.8 m/s^2.

2. Normal force: The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, since the sled is on a horizontal surface, the normal force is equal in magnitude and opposite in direction to the force of gravity.

3. Friction force: The friction force acts parallel to the surface and opposes the motion of the sled. It can be calculated as Ff = coefficient of friction * normal force. Since the coefficient of kinetic friction is given as 0.260 and the normal force is equal to the force of gravity, the friction force would be Ff = 0.260 * (18.0 kg * 9.8 m/s^2).

4. Tension in the rope: The tension in the rope can be determined by considering the equilibrium of forces along the direction of the rope. Since the sled is being pulled at a constant speed, the tension in the rope must be equal in magnitude and opposite in direction to the friction force. Therefore, the tension in the rope would be equal to the friction force.

Now, we can plug in the given values to calculate the tension in the rope:

Tension in the rope = Friction force = Ff = 0.260 * (18.0 kg * 9.8 m/s^2)

Calculate the tension in the rope using the given information and the above equation to get the final answer.