A motorcycle racer traveling at 145 km/h loses control in a corner of the track and slides across the concrete surface. The combined mass of the rider and bike is 243 kg. The steel of the motorcycle rubs against the concrete road surface. (a) What is the frictional force between the road and the motorcy- cle and rider? (b) What would be the acceleration of the motorcycle and rider during the wipeout? (c) Assuming there were no barriers to stop the motorcycle and rider, how long would it take the bike and the rider to slow to a stop?
data:
V= 145 km/h x 1000 m/1 km x 1 h/3600 s = 40.28 m/s
M=243 kg
U=0.30 (coefficient of friction from the book)
solution:
a) Weight= m.g (gravity); W=243 kg x 9.80 m/s2
W=2381.4 N
Fnet-W=0 ; Fnet=W
(friction) Fr= u.Fnet
Fr=0.30 x 2381.4 N
Fr=714.4 N
b) Fr-F=0; Fr=F
F=m x a
a= F/m
a= 714.4 N(kg.m/s2) /243 kg
a= -2.9 m/s2 (negative because is deceleration)
c) F=m.v/t
t=m.v/F
t=243 kg x 40.28 m/s / 714 ( kg x m/s2)
t = 13.7 s
you need the coefficient of friction to solve this
Actually, you don't need the coefficent of friction, you need the distance he slid, or the time.
Vf^2=vi^2 + 2ad but a=forcefriction/mass
and if you knew distance d, you could solve for forcefriction
To find the answers to these questions, we need to use the principles of friction and Newton's second law of motion.
(a) The frictional force between the road and the motorcycle/rider can be calculated using the equation:
Frictional force = coefficient of friction * normal force
The coefficient of friction depends on the materials in contact. In this case, the steel of the motorcycle rubbing against the concrete road surface would have a higher coefficient of friction compared to other materials.
Given that the combined mass of the rider and bike is 243 kg, we can calculate the normal force acting on them using the equation:
Normal force = mass * acceleration due to gravity
Acceleration due to gravity is approximately 9.8 m/s^2.
Once we have the normal force, we can multiply it by the coefficient of friction to get the frictional force.
(b) To find the acceleration of the motorcycle and rider during the wipeout, we can use Newton's second law of motion:
Force = mass * acceleration
In this case, the force acting on the motorcycle and rider is the frictional force calculated in part (a). The mass is the combined mass of the rider and bike.
Rearranging the formula, we can solve for acceleration:
Acceleration = Force / mass
(c) To determine the time it would take for the bike and rider to slow to a stop, we need to find the deceleration of the vehicle. Deceleration is simply the negative of acceleration because it opposes motion.
Once we have the deceleration, we can use the following formula to calculate the time:
Time = (final velocity - initial velocity) / deceleration
Since the motorcycle and rider are sliding without brakes applied, the deceleration is due to the frictional force acting against the motion.
Let's plug in the values and calculate the answers.