A 66.0 kg rider sitting on a 7.1 kg bike is riding along at 9.4 m/s in the positive direction. The rider drags a foot on the ground and slows down to 6.5 m/s still in the positive direction. What is the change in momentum of the rider and bike?
Δp=(m1+m2)Δν=(66+7.1)(9.4-6.5)=202 kg•m/s
To find the change in momentum of the rider and bike, we can use the equation:
Change in momentum = final momentum - initial momentum
The momentum of an object can be calculated using the equation:
Momentum = mass * velocity
Let's calculate the initial and final momentum of the rider and bike:
Initial velocity = 9.4 m/s
Final velocity = 6.5 m/s
Mass of the rider = 66.0 kg
Mass of the bike = 7.1 kg
Initial momentum of the rider and bike = mass of rider * initial velocity
= 66.0 kg * 9.4 m/s
= 619.4 kg·m/s
Final momentum of the rider and bike = mass of rider * final velocity
= 66.0 kg * 6.5 m/s
= 429.0 kg·m/s
Now, we can calculate the change in momentum:
Change in momentum = final momentum - initial momentum
= 429.0 kg·m/s - 619.4 kg·m/s
= -190.4 kg·m/s
The change in momentum of the rider and bike is -190.4 kg·m/s.
To calculate the change in momentum of the rider and bike, we need to first calculate their initial momentum and then their final momentum. The change in momentum is the difference between the final momentum and the initial momentum.
1. Calculate the initial momentum:
Momentum (p) = mass (m) × velocity (v)
For the rider:
Initial momentum of the rider (prider_initial) = mass of the rider × initial velocity of the rider
prider_initial = 66.0 kg × 9.4 m/s
For the bike:
Initial momentum of the bike (pbike_initial) = mass of the bike × initial velocity of the bike
pbike_initial = 7.1 kg × 9.4 m/s
2. Calculate the final momentum:
For the rider:
Final momentum of the rider (prider_final) = mass of the rider × final velocity of the rider
prider_final = 66.0 kg × 6.5 m/s
For the bike:
Final momentum of the bike (pbike_final) = mass of the bike × final velocity of the bike
pbike_final = 7.1 kg × 6.5 m/s
3. Calculate the change in momentum:
Change in momentum of the rider (Δprider) = prider_final - prider_initial
Change in momentum of the bike (Δpbike) = pbike_final - pbike_initial
Now you can substitute the values into the formulas and calculate the change in momentum for both the rider and the bike.