Your car is stuck in a mud hole. You are alone but you have a long strong rope. having studied physics you tie the rope tautly to a telephone pole and pull on it sideways at the midpoint as shown. Find the force exerted by the rope on the car when the anle is 3.2 and you are pulling with a force of 392 N but the car does not move. answer in units of Kn
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Your car is stuck in a mud hole. You are alone but you have a long strong rope. having studied physics you tie the rope tautly to a telephone pole and pull on it sideways at the midpoint as shown. Find the force exerted by the rope on the car when the angle is 3.1 and you are pulling with a force of 407 N but the car does not move. answer in units of Kn
To find the force exerted by the rope on the car, we can use the concept of vector components.
Let's consider the given scenario. The angle between the rope and the horizontal direction is 3.2 degrees, and you are pulling with a force of 392 N.
First, we need to find the horizontal and vertical components of the force applied to the rope.
The horizontal component (Fx) can be calculated as:
Fx = Force * cos(angle)
= 392 N * cos(3.2°)
The vertical component (Fy) can be calculated as:
Fy = Force * sin(angle)
= 392 N * sin(3.2°)
Since the car does not move, the force exerted by the rope on the car must be equal in magnitude and opposite in direction to the force being applied by you.
Therefore, we have:
Force exerted by the rope on the car = -392 N
Converting the force to kilonewtons (Kn), we divide the force by 1000:
Force exerted by the rope on the car = -392 N / 1000
≈ -0.392 Kn
Hence, the force exerted by the rope on the car when the angle is 3.2 degrees and you are pulling with a force of 392 N is approximately -0.392 Kn. Note that the negative sign indicates that the force is being exerted in the opposite direction to your pulling force.
To find the force exerted by the rope on the car, we can analyze the tension in the rope when it is pulled at an angle of 3.2 degrees with a force of 392 N.
First, let's consider the forces acting on the car. We have the weight of the car pulling it down vertically, the force you are applying horizontally, and the tension in the rope. Since the car does not move, the horizontal component of the tension in the rope must be equal to your applied force.
To determine the tension in the rope, we can break it down into its vertical and horizontal components. The horizontal component of the tension is responsible for countering your applied force, while the vertical component balances the weight of the car.
Since the car is not moving, the vertical component of the tension equals the weight of the car. However, we are only interested in the horizontal component of the tension, so let's calculate that.
The horizontal component of the tension can be found using trigonometry. Since the angle between the rope and the horizontal is 3.2 degrees, we can use the equation:
Horizontal component = Tension * cos(angle)
where Tension is the magnitude of the tension in the rope. Plugging in the values:
Horizontal component = Tension * cos(3.2°)
Now, we know that the horizontal component of the tension is equal to the applied force of 392 N:
392 N = Tension * cos(3.2°)
To solve for the tension, we can rearrange the equation:
Tension = 392 N / cos(3.2°)
Using a calculator, we find:
Tension ≈ 402.427 N
Finally, we convert the tension from Newtons to kilonewtons (kN) by dividing by 1000:
Tension ≈ 0.402 kN
Therefore, the force exerted by the rope on the car is approximately 0.402 kN.