What name is given to force A? Determine the distance travelled by the cyclist between Y and Z - AQA - GCSE Physics - Question 7 - 2021 - Paper 1

To determine the distance travelled by the cyclist, we first find the area under the motion graph provided in Figure 13. The area of the rectangle formed by the speed and time intervals gives us one part of the total distance. The area of the triangle gives us the remaining distance traveled.

1. Calculate the area of the rectangle:
   Area = length × width
   = base (time) × height (speed) = 9 m × 12 m = 108 m.

2. Calculate the area of the triangle:
   Area = rac{1}{2} × base (time) × height (speed) = rac{1}{2} × 6 m × 18 m = 54 m.

3. Total distance = Area of rectangle + Area of triangle = 108 m + 54 m = 162 m.

Thus, the distance travelled by the cyclist between Y and Z is 162 m.

The force applied on the pedal generates a moment about the pedal axle. This force creates a torque effect which translates to a rotational force about the rear axle. The force on the pedal results in a tension along the chain connected to gear B, which then exerts a force on the rear wheel, causing it to rotate. Therefore, the action of the pedal causes a rotational moment that accelerates the bicycle forward.

To find the initial acceleration of the cyclist, we can use the formula for uniform acceleration,

a = rac{v_f - v_i}{t}, where:
v_f = final velocity = 2.4 m/s
v_i = initial velocity = 0 m/s

We also know that the cyclist travelled a distance (s) of 0.018 km, which is 18 m.
To find the time (t), we can use the equation:

d = v_i*t + rac{1}{2} a t^2.

Substituting , 18 = 0 + rac{1}{2} a t^2, leading to a = rac{2d}{t^2}.

Knowing that distance, acceleration, and final speed can be used to find time, we can set up the two equations:

1. Total time to cover 18m at 2.4 m/s = 18m / 2.4m/s = 7.5s (this is a simple average estimation for time in uniform acceleration).
2. Plugging back into our formula for acceleration gives:
   a = rac{2 × 18}{(7.5)^2} = 0.16 m/s². Thus, the initial acceleration of the cyclist is 0.16 m/s².

To find the resultant force, we can use vector addition to combine the horizontal and vertical components.

1. Draw the horizontal force (200 N) to the right and the vertical force (75 N) upward to create a right triangle.

2. The magnitude of the resultant force can be calculated using the Pythagorean theorem:

   Resultant force (R) = $oot{2}{(200^2 + 75^2)}$ = $oot{2}{(40000 + 5625)}$ = $oot{2}{45625}$ ≈ 214 N.

3. To find the direction (θ) of the resultant force, use the tangent function:

   an(θ) = rac{vertical}{horizontal} = rac{75}{200}

   Therefore,
   θ = an^{-1}igg(rac{75}{200}igg) ≈ 20.22° from the horizontal.

So, the magnitude of the resultant force is approximately 214 N, and its direction is about 20° from the horizontal.