Question

KC has a piece of gum stuck to her bike tire, which applies a forward torque (i.e. a force to roll forwards) on the tire's movement. The torque varies in a periodic way that can be modeled approximately by a trigonometric function. When the gum is on the front of the tire, its weight is pulling forwards with a maximum torque of 0.01 Nm (Newton metre, the SI unit for torque), and when it's on the back of the tire, it's pulling backwards with a minimum torque of -0.01 Nm. The maximum torque is reached once in every rotation, which is every 1.2 meters. The first time it reaches its maximum torque is 0.3 meters into the race. Find the formula of the trigonometric function that models the torque the gum applies on the tire d meters into the race. Define the function using radians. What is the torque when KC has ridden 4 meters? Round your answer, if necessary, to four decimal places.

Answer 1

Step-by-step explanation:

amplitude=0.01

then the function starts at after 0.3 at y=0 therefore cosine function should be used.

period =1.2 m

horizontal phase shift = -0.3

vertical phase shift =nil

Therefore the function is 0.01 cos{2π÷1.2(d-0.3)}

substituting d=4 m

answer is 0.0087(approx)