A cyclist is coasting at a steady speed of 17m/s but enters a muddy stretch where the effective coefficient of friction is 0.60.
What will be the speed upon emerging?
You need the length of muddy stretch ‘s’
ma=F(fr) =μmg,
=> a= μg.
a=(v² -v₀²)/2s
μg=(v² -v₀²)/2s
v= sqrt(2sμg+ v₀²)
How long is the "muddy stretch"?
Are the bike tires rolling or skidding?
Whoever assigned this question apparently does not understand rolling motion.
Elena apparently does not take into account that unless a tire is skidding, the friction at the point of contact does not slow the bike down. The point of contact is an instant center, kinematically speaking.
To answer this question, we need to understand the concept of the effective coefficient of friction and how it affects the speed of the cyclist.
The effective coefficient of friction represents the resistance to motion experienced by an object when it comes into contact with a surface. In this case, the muddy stretch acts as the surface causing the cyclist to experience a change in speed.
To calculate the speed upon emerging from the mud, we need to consider the forces acting on the cyclist. The primary force that affects the cyclist's speed is the force of friction, which can be calculated using the equation:
Friction force = coefficient of friction × normal force
In this scenario, the normal force acting on the cyclist is equal to the cyclist's weight, as gravity acts directly downward. The formula for the weight of an object is:
Weight = mass × gravity
Assuming the mass of the cyclist is constant, the weight remains unchanged. Therefore, the normal force remains constant as well.
Once we calculate the force of friction, we can use Newton's second law of motion to determine the acceleration experienced by the cyclist. Newton's second law states that the net force acting on an object is equal to the product of its mass and acceleration:
Net force = mass × acceleration
In this case, the net force is the force of friction, and rearranging the formula gives us:
Acceleration = force of friction / mass
Since the cyclist is coasting at a steady speed, we can assume that the acceleration upon entering the muddy stretch is zero. This means the force of friction must be equal to the opposing force of the cyclist's original momentum.
Using the equation:
Force of friction = mass × acceleration
We can rewrite it as:
Force of friction = mass × (final velocity - initial velocity) / time
Since the acceleration is zero, the formula becomes:
Force of friction = mass × (final velocity - initial velocity) / time
Now we can substitute the values given in the question into the equation:
Force of friction = mass × (final velocity - 17 m/s)
To find the final velocity upon emerging, we need to isolate the final velocity in the equation. We can do this by rearranging the formula:
Final velocity = (Force of friction / mass) + initial velocity
Final velocity = (0.60 × mass × gravity / mass) + 17 m/s
Mass cancels out, giving us:
Final velocity = (0.60 × gravity) + 17 m/s
Now, we need to know the value of gravity, which is approximately 9.8 m/s² on Earth. Plugging in this value:
Final velocity = (0.60 × 9.8 m/s²) + 17 m/s
Now, we can simply calculate the value:
Final velocity = 5.88 m/s + 17 m/s
Final velocity = 22.88 m/s
Therefore, the speed upon emerging from the muddy stretch would be approximately 22.88 m/s.