Questions: 4 x^2+x^2 Ftext nee = 1 speed:

4 x^2+x^2 Ftext nee = 1 speed:
Transcript text: $4 x^{2}+x^{2}$ \[ \left|F_{\text {nee }}\right|=\square 1 \] speed: $\square$
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Solution

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Solution Steps

Step 1: Identify the forces

The free-body diagram shows four forces acting on the cyclist:

  • N: Normal force (upward) = N
  • W: Weight (downward) = 650 N
  • D: Drag force (leftward) = 50 N
  • Th: Thrust (rightward) = 120 N
Step 2: Calculate Net Vertical Force

The net vertical force is the difference between the normal force (N) and the weight (W). Since the cyclist is not accelerating vertically, these forces must be equal. Therefore:

N = W = 650 N

Step 3: Calculate Net Horizontal Force

The net horizontal force is the difference between the thrust (Th) and the drag force (D):

$F_{net,x} = Th - D = 120 N - 50 N = 70 N$

Step 4: Calculate the Magnitude of the Net Force

Since the net vertical force is zero, the magnitude of the net force is equal to the net horizontal force:

$|F_{net}| = \sqrt{F_{net,x}^2 + F_{net,y}^2} = \sqrt{70^2 + 0^2} = 70 N$

Step 5: Determine the direction of the net force

The net force is in the positive x-direction (to the right) since it's positive.

Step 6: Analyze the speed

Since there is a net force acting on the cyclist, they are accelerating. A net force to the right means the cyclist is speeding up. We cannot calculate the _value_ of the speed without knowing the cyclist's mass and the time elapsed.

Final Answer:

Magnitude of net force: \\(\boxed{70 \text{ N}}\\) Speed: increasing

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