Tension in Rope: Truck Towing 1T Car Up Hill

In summary, the conversation discusses a truck towing a car up a hill with a rope attached at an angle of 10 degrees with respect to the horizontal. The question is posed about the tension in the rope and whether the sum of the x and y components should be zero or not. The conversation concludes that since the truck is moving at a constant speed, the sum of the components in any direction must be zero. The normal force and weight are also mentioned as factors to consider in calculating the tension in the rope.
  • #1
milo7979
3
0
A truck is towing a 1.00*10^3 kg car at a constant speed up a hill that makes an angle of 5degrees with respect to the horizontal. A rope (negligable) is attached to the truck at an angle of 10 degrees with respect to the horizontal. Neglect friction. What is the tension in the rope?
I'm not sure if the sum of the x and y components should be zero or not?
 
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  • #2
Welcome to PF!

milo7979 said:
A truck is towing a 1.00*10^3 kg car at a constant speed up a hill that makes an angle of 5degrees with respect to the horizontal. A rope (negligable) is attached to the truck at an angle of 10 degrees with respect to the horizontal. Neglect friction. What is the tension in the rope?
I'm not sure if the sum of the x and y components should be zero or not?

Hi milo7979! Welcome to PF! :smile:

Constant speed means zero acceleration …

so, yes, the sum of the components in any direction must be zero. :smile:

(though you might find it easier to use components along the slope :wink:)
 
  • #3
i thought about using different coordinates, but only one of the forces will be on the axis because there are three forces with different angles with respect to the horizontal. I can't seem to get all of the y components to equal zero. The y component of the normal force I assume is the same magnitude as the weight (1.0*10^3 * g= 9.8*10^3N), but there is still a y component to the Force from the truck. W and y component of N equal zero, so what am I missing?
 
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  • #4
milo7979 said:
i thought about using different coordinated, but only one of the forces will be on the axis because there are three forces with different angles with respect to the horizontal.

Yes, there are three forces, and two of them are along the slope and perpendicular to it … :wink:
 
  • #5
I don't think that two of the forces are along the x and y axis. N is perpendicular to the hill which is 5 degrees to the left of vertical, W which is straight down the vertical and F of truck pulling the car is 10 degrees above horizontal.
 
  • #6
milo7979 said:
I don't think that two of the forces are along the x and y axis. N is perpendicular to the hill which is 5 degrees to the left of vertical, W which is straight down the vertical and F of truck pulling the car is 10 degrees above horizontal.

oh, sorry :redface: …

I misread it …

ok, the force you want is the tension in the rope, so calulate the normal force, and then take components of everything along the line of the rope. :smile:
 

What is tension in rope?

Tension in rope is the force applied to a rope when it is being pulled or stretched. In the context of truck towing a car uphill, tension in the rope is the force applied by the truck to the rope in order to move the car.

Why is tension in rope important in truck towing?

Tension in the rope is important in truck towing because it determines the maximum weight that can be towed and the amount of force required to move the towed vehicle. If the tension in the rope is not enough, the car may not move or may move very slowly.

What factors affect tension in rope during truck towing?

The factors that affect tension in rope during truck towing include the weight of the car being towed, the angle of the incline, the condition of the road, and the strength and elasticity of the rope being used.

How can tension in rope be calculated during truck towing?

Tension in rope can be calculated using the formula T = mg + ma, where T is the tension, m is the mass of the car, g is the acceleration due to gravity, and a is the acceleration of the car. This formula takes into account the weight of the car and the force required to move it uphill.

What are some safety precautions to consider when using tension in rope for truck towing?

When using tension in rope for truck towing, it is important to make sure that the rope is securely attached to both the truck and the car, and that it is not frayed or damaged. It is also crucial to maintain a safe distance between the two vehicles and to use caution when driving on steep inclines. Additionally, it is important to follow all laws and regulations regarding truck towing and to have the necessary training and experience to safely operate the vehicles involved.

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