Linearization and Physics

Question

A 2-kg ball is falling and a radar gun records its velocity as v = 5 m/sec. This radar gun has an error of ±0.2 m/sec, meaning the difference between the ball’s actual speed and the value the radar gun records is at most 0.2 m/sec. The ball’s kinetic energy is given by the equation:

KE = 1/2 m v^2

(a) Use the radar gun’s measurement to calculate the ball’s kinetic energy.

(b) Estimate the error in the computed value of kinetic energy.

(c) Find the linearization L(v) of the kinetic energy, thought of as a function of velocity

Answer 1

Hopefully this is from a calculus-based physics or physics lab that includes error analysis. Part (a) is extremely straight-forward and only requires substitution of given values into your equation for kinetic energy K = 0.5mv².

Here the kinetic energy equation can be considered one-variable (v) if the mass is not changing, i.e., it’s not losing/gaining mass while falling. To answer (b) ultimately you will end up with your “delta K” (error propagated in KE calculation) as 2*0.5*m*v* “delta v”. “Delta v” in this case is 0.2 m/s.

Answer 2

KE=.5(2mg)(5ms)^2=25

As for error; the gravitational pull is needed; which is 32.2 (ft/sec)^2 or (9.81m/s)^2.