a bicyclist and his bike have a combined mass of 105 kg. He is traveling at 15.0 m/s along the path when he sees a fallen tree 4 m in front of him. In order to stop before hits the tree, find the boy's minimum acceleration and the minimum force that must be applied.
Thank You!!!
Use (Vf)^2 = (Vi)^2 + 2as
where Vf is final velocity, Vi is the initial velocicy, a is acceleration, and s is distance.
To find the minimum acceleration and minimum force required for the bicyclist to stop before hitting the tree, we can use the kinematic equation you provided: (Vf)^2 = (Vi)^2 + 2as.
Given:
Total mass of the bicyclist and bike, m = 105 kg
Initial velocity, Vi = 15.0 m/s
Distance to be covered, s = 4 m
We need to find:
Minimum acceleration, a
Minimum force, F
Step 1: Find the final velocity (Vf) using the kinematic equation.
(Vf)^2 = (Vi)^2 + 2as
(Vf)^2 = (15.0 m/s)^2 + 2(-a)(4 m)
(Vf)^2 = 225 m^2/s^2 - 8as
Since the bicyclist needs to stop before hitting the tree, the final velocity (Vf) would be 0 m/s.
Setting (Vf)^2 = 0 gives us:
0 = 225 m^2/s^2 - 8as
Step 2: Rearrange the equation to solve for acceleration (a).
8as = 225 m^2/s^2
a = 225 m^2/s^2 / 8s
a = 28.125 m/s^2
So, the minimum acceleration required for the bicyclist to stop before hitting the tree is 28.125 m/s^2.
Step 3: Calculate the minimum force using Newton's second law: F = ma.
Given mass, m = 105 kg
Acceleration, a = 28.125 m/s^2
F = (105 kg)(28.125 m/s^2)
F = 2953.125 N
Therefore, the minimum force that must be applied to stop the bicyclist before hitting the tree is 2953.125 N.