Question

A student is riding their bike when they come across a turn in the form of a circular arc of radius R 3.0m as pictured in the diagram below and travel along this arc in the clockwise direction. At one point along this trajectory (the origin of the given coordinate system) it makes sense to define the Cartesian coordinate system shown where the x-axis is tangent to the trajectory and the y-axis is perpendicular to it. At this point the acceleration of the combined student-bike system (referred to simply as the "student" from now on since this system can be treated as a single entity) has a magnitude of 17m/s2 and forms an angle of 62o below the negative x-axis as depicted in the diagram. It was previously found that at this point the student is slowing down and their acceleration, a, in the given coordinate system is a -(-8.0m/s2)1 + (-15m/s2)). 62 1. In this situation it's known that there are two different types of friction forces acting on the student (really they act specifically on the bike but the entire student-bike system is being referred to as the student in this case) which can be treated as independent. There's kinetic friction which acts tangent to their trajectory (meaning along the x-axis here) and then there's static friction which acts perpendicular to their trajectory (meaning along the y-axis here) (a) (4 points) If the student has a mass of 75kg find the net force acting on them in î,J, K notation. (b) (6 points) Draw a free body diagram for the student (who can be labeled S) that only shows forces acting in the x and y directions (the gravitational and normal forces on the student both act in the z-direction and don't need to be shown) next to the diagram above while clearly indicating which way the positive x-axis and the positive y-axis point. The ground that the student is riding on can be labeled QG 2. (a) (5 points) Find the kinetic friction force acting on the student in I,], K notation (b) (4 points) Find the magnitude of the normal force acting on the student (it might be helpful to draw a free body diagram showing the x-direction and the z-direction but not the y-direction). (c) (5 points) Find the coefficient of kinetic friction between the bike's tires and ground (uk) 3. (6 points) Assuming that kinetic friction acts tangent to the student's trajectory (and opposite their direction of motion) for the entire time that they're traveling along this circular arc and that static friction acts perpendicular to their trajectory for this entire time, is the work done by kinetic friction during this time period positive, negative, or zero? How do you know? Is the work done by static friction during this time period positive, negative, or zero? How do you know?

Answer 1

An s 62° a) - o sin 6 sin 62。 13x 5 ms