A popular daredevil trick is to complete a vertical loop on a motorcycle. This trick is dangerous, however, because if the motorcycle does not travel with enough speed, the rider falls off the track before reaching the top of the loop. What is the minimum speed necessary for a rider to successfully go around a vertical loop of 10 meters?
Ah, the thrilling world of daredevil tricks! Well, my speed demon friend, let's calculate the minimum speed required for this gravity-defying feat.
To successfully complete the loop, the rider should experience a minimum acceleration equal to the gravitational acceleration (9.8 m/s²) plus an extra bit to keep them securely on the track. We can use some physics magic to figure out this speed.
The centripetal force required for the rider can be given by the equation:
Fc = m * (v² / r)
Where Fc is the centripetal force, m is the mass of the rider, v is the velocity, and r is the radius of the loop (half the diameter).
Now, the gravitational force acting on the rider is given by:
Fg = m * g
Where Fg is the gravitational force and g is the acceleration due to gravity (9.8 m/s²).
To successfully complete the loop, the centripetal force must be greater than or equal to the gravitational force:
Fc ≥ Fg
After substituting the equations, we get:
m * (v² / r) ≥ m * g
Canceling out the mass, we find:
v² / r ≥ g
Now, rearranging the equation to solve for v, we have:
v ≥ √(g * r)
Substituting in the given values, with r = 10 meters, we find:
v ≥ √(9.8 m/s² * 10 m)
Calculating that out, we get:
v ≥ √(98 m²/s²)
And finally:
v ≥ 9.899 m/s
So, my friend, the minimum speed required to successfully complete the vertical loop of 10 meters is approximately 9.899 m/s. Keep in mind that this is just a minimum, so go ahead and add a little extra speed for some margin of safety. And stay safe out there, high-flying daredevil!
To determine the minimum speed required for a rider to complete a vertical loop, we need to consider the forces acting on the rider at the top of the loop. At the top, the rider needs to achieve sufficient speed to counteract the force of gravity.
The rider's speed at the top of the loop can be determined using the centripetal force formula:
F_c = m * v^2 / r
where:
F_c is the centripetal force,
m is the mass of the rider,
v is the velocity of the rider, and
r is the radius of the loop.
In this case, the centripetal force is equal to the force of gravity acting on the rider:
F_c = m * g
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Setting these two equations equal to each other, we can solve for the velocity (v):
m * v^2 / r = m * g
Canceling out the mass (m) on both sides, we get:
v^2 / r = g
Rearranging the equation, we find:
v^2 = g * r
Finally, taking the square root of both sides, we find:
v = sqrt(g * r)
Given that the radius of the loop is 10 meters, we can calculate the minimum speed required:
v = sqrt(9.8 m/s^2 * 10 m) = sqrt(98 m^2/s^2) = 9.9 m/s
Therefore, the minimum speed necessary for a rider to successfully complete a vertical loop of 10 meters is 9.9 meters per second.
To determine the minimum speed necessary for a rider to successfully go around a vertical loop, we can use the concept of centripetal force. This force keeps an object moving in a circular path and is calculated as the product of the mass of the object, the square of its velocity, and the radius of the circular path.
In this scenario, the radius of the loop is 10 meters. To find the minimum speed, we need to ensure that the centripetal force is equal to or greater than the force of gravity acting on the rider.
The force of gravity can be calculated using the formula: force = mass x acceleration due to gravity. On Earth, the acceleration due to gravity is approximately 9.8 m/s².
The centripetal force (Fc) can be calculated using the formula: Fc = mass x velocity² / radius.
Since we are looking for the minimum speed necessary to complete the loop, we'll assume that the force of gravity is equal to the centripetal force at the top of the loop. Therefore, we can set up the equation:
mass x acceleration due to gravity = mass x velocity² / radius
The mass cancels out, and we can rearrange the equation to solve for velocity:
velocity = √(radius x acceleration due to gravity)
Plugging in the given values for the radius (10 meters) and acceleration due to gravity (9.8 m/s²):
velocity = √(10 x 9.8) m/s
velocity = √(98) m/s
velocity ≈ 9.9 m/s
Therefore, the minimum speed necessary for a rider to successfully go around a vertical loop of 10 meters is approximately 9.9 meters per second.
mg=m*v^2/r
Vmin=sqrt(g*r)= sqrt(9.8*10)
=9.9m/s