A 60kg biker on a 20kg bike exerts 600W of power to accelerate from 1m/s to 9m/s in a distance of 40m. What is the force of friction acting on the bike and biker?
To find the force of friction acting on the bike and biker, we need to consider the work done, power, and acceleration.
The work done can be calculated using the formula: work = force × distance.
In this case, the work done is equal to the change in kinetic energy. The change in kinetic energy is given by the formula: change in kinetic energy = 0.5 × mass × (final velocity^2 - initial velocity^2).
Given:
- Mass of the biker (m1) = 60 kg
- Mass of the bike (m2) = 20 kg
- Initial velocity (u) = 1 m/s
- Final velocity (v) = 9 m/s
- Distance (s) = 40 m
- Power (P) = 600 W
First, let's calculate the change in kinetic energy:
change in kinetic energy = 0.5 × (m1 + m2) × (v^2 - u^2)
= 0.5 × (60 kg + 20 kg) × (9 m/s)^2 - (1 m/s)^2
= 0.5 × 80 kg × (81 m^2/s^2 - 1 m^2/s^2)
= 0.5 × 80 kg × 80 m^2/s^2
= 0.5 × 80 kg × 80 J
Next, let's calculate the work done:
work = force × distance
= change in kinetic energy
Since the power is given by the formula: power = work / time,
we can rearrange the formula to calculate time:
time = work / power
Substituting the values, we get:
time = (0.5 × 80 kg × 80 J) / (600 W)
= (0.5 × 80 kg × 80 J) / (600 J/s)
= (0.5 × 80 kg) / (600 / 80) s
= 0.5 × 80 kg × (80 / 600) s
= 0.5 × 80 kg × (4 / 30) s
= 0.5 × 80 kg × (2 / 15) s
= 2 / 15 × 80 kg
So, the time taken is (2 / 15) × 80 kg seconds.
Now, we can calculate the force using the formula: force = mass × acceleration.
In this case, the acceleration can be calculated using the formula: acceleration = change in velocity / time.
change in velocity = final velocity - initial velocity
= 9 m/s - 1 m/s
= 8 m/s
acceleration = (change in velocity) / (time)
= 8 m/s / [(2 / 15) × 80 kg]
= 8 m/s ÷ (16 / 15) m/s²
= 8 m/s × (15 / 16) s²
= 120 / 16 m/s²
= 7.5 m/s²
Finally, we can calculate the force of friction:
force = (mass of biker + mass of bike) × acceleration
= (60 kg + 20 kg) × 7.5 m/s²
= 80 kg × 7.5 m/s²
= 600 N
Therefore, the force of friction acting on the bike and biker is 600 Newtons.