X and y components in force problem

In summary, the problem involves a 10 kg sled being pulled by a force of 100 N at an angle of 35 degrees east of north, with an additional force of 150 N directed due east and a friction force of 50 N. The question is how to properly draw out the x and y components of the angled force in order to determine the sled's acceleration (both magnitude and direction). The tension force (Ft) is known to be 100 N and can be broken down into east and north components using trigonometry.
  • #1
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The problem is:
A 10 kg sled is pulled at an angle of 35 o east of north by a force of 100 N and with a force of 150 N directed due east. A friction force of 50 N acts as well. What is the acceleration (both magnitude and direction of the sled.

My question - could someone help me properly draw out the x and y components of the angled Force ? Thanks in advance
 
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  • #2
The Tension Force (Ft) is in the direction of the rope and you are told that the total Ft=100 N

So you want to figure out the east and north components of this force. Draw a triangle with the hypotenuse as Ft=100 N

To get the east component, you want to take cos(180-35) because cos(x)=adjacent(east)/hypotenuse , now solve for the adjacent(east) component. You can do the same to get the north component, but by using sin(x)=opposite(north)/hypotenuse
 

1. What are X and Y components in force problem?

X and Y components in force problem refer to the division of a force vector into its horizontal and vertical components. This is done in order to simplify the problem and make it easier to solve using mathematical equations.

2. How do you calculate the X and Y components of a force vector?

The X and Y components of a force vector can be calculated using trigonometric functions. To find the X component, multiply the magnitude of the force by the cosine of the angle it makes with the horizontal axis. To find the Y component, multiply the magnitude of the force by the sine of the angle.

3. Why is it important to break down forces into X and Y components?

Breaking down forces into X and Y components allows us to apply the rules of trigonometry and solve the problem using simple mathematical equations. It also helps us to understand the direction and magnitude of the force acting on an object more clearly.

4. Can the X and Y components of a force vector have negative values?

Yes, the X and Y components of a force vector can have negative values. This indicates that the force is acting in the opposite direction of the positive axis. For example, a force acting downwards will have a negative Y component.

5. How do you find the resultant force from the X and Y components?

The resultant force can be found by using the Pythagorean theorem. The magnitude of the resultant force is equal to the square root of the sum of the squares of the X and Y components. The direction of the resultant force can be found by taking the inverse tangent of the Y component divided by the X component.

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