A cyclist is coasting at a steady speed of 17 but enters a muddy stretch where the effective coefficient of friction is 0.60. a)Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 23?
b)What will be the speed upon emerging?
There are no units on the numerals. I have no idea what they represent.
To answer these questions, we need to consider the forces acting on the cyclist and apply Newton's second law of motion.
a) Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 23 seconds?
To determine if the cyclist can coast through the muddy stretch without pedaling, we need to evaluate the net force acting on the cyclist.
The main force in this case is the force of friction between the muddy stretch and the bicycle tires. The formula to calculate the force of friction is:
Force of friction = coefficient of friction * normal force.
The normal force is the force exerted by the ground perpendicular to the contact surface, which is equal to the weight of the cyclist and the bicycle.
Normal force = mass of cyclist * acceleration due to gravity.
Assuming the mass of the cyclist is 70 kg and the acceleration due to gravity is 9.8 m/s^2, the normal force can be calculated as:
Normal force = 70 kg * 9.8 m/s^2 = 686 N.
Now we can calculate the force of friction:
Force of friction = 0.60 * 686 N = 411.6 N.
Since the cyclist is coasting at a steady speed, there is no external force applied (such as pedaling). Therefore, the net force acting on the cyclist is zero.
Now, if the force of friction is greater than the net force (zero), the cyclist will decelerate and eventually come to a stop. However, if the force of friction is less than or equal to the net force, the cyclist will be able to continue coasting without pedaling.
In this case, since the force of friction (411.6 N) is less than the net force (zero), the cyclist will indeed emerge from the muddy stretch without having to pedal.
b) What will be the speed upon emerging?
To calculate the speed upon emerging from the muddy stretch, we need to find the acceleration during the muddy stretch. We can use Newton's second law of motion:
Net force = mass * acceleration.
Since the net force is zero (coasting at a steady speed), the equation becomes:
0 = mass * acceleration.
Solving for acceleration:
acceleration = 0 m/s^2.
Since the acceleration is zero, the cyclist's speed will remain constant, and there will be no change upon emerging from the muddy stretch. So the speed upon emerging will still be 17 m/s.