What Does the 'Kissing Circle' Reveal About Momentum and Net Force?

[Nal101]

The "kissing circle"

Homework Statement

An object moving at a constant speed of 31 m/s is making a turn with a radius of curvature of 4 m (this is the radius of the "kissing circle"). The object's momentum has a magnitude of 87 kg·m/s.
What is the magnitude of the rate of change of the momentum?
What is the magnitude of the net force?

Homework Equations

p = mv
$$\Delta$$p = F_net$$\Delta$$t
dp/dt = magnitude of V / R (sry don't know how to put that in latex)

The Attempt at a Solution

Question 1: Velocity divided by radius? Using the 3rd equation, but the units don't check out.
I am lost
Question 2: How do I find t, and afterwards, the answer would be F_net = 87 (change in momentum) * t (change in time)

 

[rock.freak667]

the rate of change of momentum is just acceleration so you need to find the centripetal acceleration.

 

[tomcue]

= 87/t

I can provide a response to the concept of the "kissing circle" in the context of the given scenario. The "kissing circle" refers to the radius of curvature in which an object is turning while maintaining a constant speed. In this case, the object is moving at a speed of 31 m/s and turning with a radius of 4 m.

To answer the first question, we can use the equation for momentum (p=mv) to calculate the magnitude of the rate of change of momentum. Since the object is moving at a constant speed, its velocity does not change, therefore the rate of change of momentum is equal to zero.

For the second question, we can use the equation \Deltap = Fnet\Deltat to find the magnitude of the net force. Rearranging the equation, we get Fnet = \Deltap/\Deltat. Since the magnitude of the change in momentum is given as 87 kg·m/s, we need to find the change in time (t) to calculate the net force. This can be done by using the equation for centripetal acceleration, a=v^2/r, and substituting the values given in the problem. Once we have the value for t, we can calculate the net force using the equation Fnet = 87/t.

In conclusion, the "kissing circle" refers to the radius of curvature in which an object is turning while maintaining a constant speed. To calculate the magnitude of the rate of change of momentum, we use the equation p=mv and for the magnitude of the net force, we use the equation Fnet = \Deltap/\Deltat.