A bicyclist is traveling at +25m/s when he begins to decelerate at -4m/s2. How fast is he traveling after 5 seconds
1 answer:
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To solve this problem it is necessary to apply the kinematic equations of angular motion.
Torque from the rotational movement is defined as
where
I = Moment of inertia For a disk
Angular acceleration
The angular acceleration at the same time can be defined as function of angular velocity and angular displacement (Without considering time) through the expression:
Where
Final and Initial Angular velocity
Angular acceleration
Angular displacement
Our values are given as
Using the expression of angular acceleration we can find the to then find the torque, that is,
With the expression of the acceleration found it is now necessary to replace it on the torque equation and the respective moment of inertia for the disk, so
Therefore the torque exerted on it is
A) 2.64 H
The maximum height that the expelled rock can reach can be found by using the equation:
where
v = 0 is the velocity at the maximum height
u is the initial velocity
g is the acceleration of gravity
d is the maximum height
Solving for d,
We see that the maximum heigth is inversely proportional to g. On the Earth,
and
So we can write:
where H' is the maximum height reached on Mars, and is the acceleration of gravity on Mars. Solving for H',
B) 2.64T
The time after which the rock reaches the maximum height can be found by using
where
v = 0 is the velocity at the maximum height
u is the initial velocity
Solving for t,
The total time of the motion is twice this value, so:
So we see that it is inversely proportional to g.
On the Earth, t = T. So we can write:
where T' is the total time of the motion on Mars. Solving for T',