The speed of a bobsled is increasing because it has an acceleration of 2.3 m/s2. At a given instant in time, the forces resisting the motion, including kinetic friction and air resistance, total 450 N. The mass of the bobsled and its riders is 230 kg.
To find the speed of the bobsled, we can use Newton's Second Law of Motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. The net force is the difference between the applied force (in this case, the force accelerating the bobsled) and the resistant forces (such as kinetic friction and air resistance).
The equation for Newton's Second law is:
F_net = m * a
Where:
F_net = Net force
m = Mass of the object
a = Acceleration
In this case, the net force is the force accelerating the bobsled minus the resistant forces:
F_net = F_applied - F_resistant
Given:
Acceleration (a) = 2.3 m/s^2
Resistant Forces (F_resistant) = 450 N
Mass (m) = 230 kg
Replacing the values in the equation, we have:
F_applied - 450 = 230 * 2.3
Now, we solve for the applied force (F_applied):
F_applied = 230 * 2.3 + 450
Calculating the value:
F_applied = 529 + 450
F_applied = 979 N
So, the applied force accelerating the bobsled is 979 N.
Now, we can use this information to find the speed of the bobsled. We can use the equation:
F_net = m * a
Since the net force is equal to the applied force, we can rewrite the equation as:
F_applied = m * a
Rearranging the equation to solve for acceleration:
a = F_applied / m
Substituting the values:
a = 979 / 230
Calculating the value:
a ≈ 4.26 m/s^2
Therefore, the acceleration of the bobsled is approximately 4.26 m/s^2.
Now, we can use another equation to find the final velocity (speed) of the bobsled. The equation for calculating final velocity is:
v = u + at
Where:
v = Final velocity
u = Initial velocity (assumed to be 0 in this case)
a = Acceleration
t = Time
Since the bobsled is starting from rest (u = 0), the equation simplifies to:
v = at
Substituting the values:
v = 4.26 * t
We do not have information about time (t) given in the question. If you provide the time, we can calculate the final velocity.