Tension on a Rope if used to Accelerate a car?

In summary, the car is driven 100 km west and then 95 km southwest, resulting in a displacement of approximately 141.4 km at an angle of 225 degrees south of west from the point of origin. To solve for the displacement, the vectors are broken down into their horizontal and vertical components, and then added together using trigonometry to form a triangle. Finally, the resulting components are added together to form the final displacement vector.
  • #1
meganw
97
0

Homework Statement



A car is driven 100 km west and then 95 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)?

________ km
________ ° south of west

Homework Equations



none? I apologize if I am overlooking any equation, but there are no equations that I know of that can help when adding vectors. Perhaps the Pythagorean theorem in some cases.

The Attempt at a Solution



I really don't understand how to add this type of vector. Generally with vectors I separate them into their horizontal and vertical components, but in this case there is no angle given really..so I think that would be impossible. (Sine/Cosine won't work without an angle!)

Thank you so much for your patience with me! I'm afraid I don't understand the concept very well...this is my first physics class, and my only knowledge of Physics is self-taught.
 
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  • #2
You already have your components, east-west can be thought of as an x compoonent and north-south as a y component.
 
  • #3
Tension on a rope? Is that another question or something?

Anyway, as far as vectors go, just think of them as triangles. For the first part the car is driven 100km west, so that is easy, and you can represent it as -100i (given that you make east and north positive). Then when the car drives 95 km southwest the car has a vector component that is west, and a vector component that is south.

Looking at the second part as a triangle, you have the 95km southwest as the hypotenuse, and so the west and south parts will be the legs. The triangle has an angle of 45 degrees, since southwest is 45 degrees south of west (or you could at it as 45 degrees west of south). So if you use trigonometry then you will figure out what the length of the legs are. Hint: they should be equal, and one will point in the -i (west) direction while another points in the -j (south) direction.

Add the like components, you have two that are pointed in the -i direction (west), and one pointed in the -j direction (south). Once you have the components added up you are back to having two legs. At this point I think you will see that this makes another triangle you can piece together with trig, and will be the triangle you are looking for.
 
  • #4
Sorry about the faulty title-I tried to go back and edit it after clicking "Submit" but the Edit Feature doesn't allow you to change the Subject Title

Mindscrape: Thank you so much for your help! I didn't realize that "southwest" could be read as 45 degrees-I thought it was just a vague direction! (Sounds silly...I know.) I am indebted to your assitance! Thanks a ton! o:)
 

1. How does tension on a rope affect the acceleration of a car?

The tension on a rope can either increase or decrease the acceleration of a car, depending on the direction of the tension force. If the tension force is in the same direction as the car's motion, it can increase the acceleration. However, if the tension force is in the opposite direction, it can decrease the acceleration.

2. What factors can affect the tension on a rope used to accelerate a car?

The tension on a rope can be affected by several factors, including the mass of the car, the acceleration of the car, the angle at which the rope is attached to the car, and the strength of the rope itself. Other factors such as friction and air resistance may also impact the tension on the rope.

3. How can you increase the tension on a rope to accelerate a car?

To increase the tension on a rope, you can either increase the force applied to the rope or decrease the mass of the car. This will result in a greater net force acting on the car, which in turn will increase the tension on the rope and accelerate the car.

4. Can too much tension on a rope be dangerous for accelerating a car?

Yes, too much tension on a rope can be dangerous for accelerating a car. If the tension force exceeds the breaking strength of the rope, it can snap and cause the car to suddenly lose acceleration. It is important to use a rope with a sufficient breaking strength to safely accelerate a car.

5. Does the length of the rope affect the tension on a rope used to accelerate a car?

The length of the rope does not directly affect the tension on a rope used to accelerate a car. However, a longer rope may result in a larger angle between the rope and the car, which can impact the direction and magnitude of the tension force. Additionally, a longer rope may also increase the amount of friction and air resistance, which can affect the tension on the rope.

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