A bicycle and rider of total weight 815 N travel at a speed of 40.0 km/h.
The rider hits the breaks and the bicycle slides to a full stop in a distance of 8.5 m.
Ignore air resistance and use g=9.8 m/s2.
What is the coefficient of kinetic friction between the tires (rubber) and the road (pavement)?
So do I use F= μ x mass of solid x g
and solve for μ
μ= F/(Mass of solid*g)
=F/815
Ok I feel as if its wrong, because I don't consider the speed or distance in this problem
I agree, something is missing. The formula is correct if you knew the force, F.
In this case, the force is not know, but you can calculate the average force from energy considerations.
Work done by friction = F*D = 8.5F
using g=9.8 m/s², kinetic energy before hitting the brakes
= (1/2)mv²
= (1/2)(815/g)(40000/3600 m/s)²
Equate kinetic energy and work done and solve for F
F = 604 N
μ = F/(mg) = 604/815 = 0.74
How did u arrive at F=604 N can you please describe/explain it more in detail.
thank you
@risha,
equate (1/2)mv^2=8.5F
m and v are known, solve for F,
therefore F=604N
To calculate the coefficient of kinetic friction between the tires and the road, you need to consider the force acting on the bicycle during the braking process. The force can be found using Newton's second law, which states that force equals mass times acceleration:
F = m * a
Since the bicycle comes to a stop, its final velocity is zero and the initial velocity is 40.0 km/h, which can be converted to meters per second (m/s) by dividing by 3.6:
v_initial = 40.0 km/h = (40.0 * 1000) m / (60 * 60) s = 11.11 m/s
The acceleration (a) can be calculated using the following equation:
a = (v_final - v_initial) / t
v_final is the final velocity (0 m/s), v_initial is the initial velocity (11.11 m/s), and t is the time it takes for the bicycle to come to a stop. However, the time is not provided in this question.
Since the distance (d) traveled during the braking process is given (8.5 m), you can use the following equation to find the time:
d = v_initial * t + (1/2) * a * t^2
By substituting the known values, you can solve for the time (t).
After finding the time it takes for the bicycle to come to a stop, you can calculate the acceleration (a). Then, using Newton's second law (F = m * a), you can find the force (F) acting on the bicycle.
Finally, you can use the equation for frictional force (F_fric = μ * N) to find the coefficient of kinetic friction (μ), where N is the normal force equal to the weight of the bicycle and rider (815 N) in this case.
To summarize the steps:
1. Convert the initial velocity from km/h to m/s.
2. Calculate the time it takes for the bicycle to come to a stop using the distance traveled and the kinematic equation.
3. Calculate the acceleration of the bicycle using the determined time and initial/final velocities.
4. Use Newton's second law to calculate the force acting on the bicycle.
5. Use the equation for frictional force to find the coefficient of kinetic friction.