Physics friction & kinetic energy problem .... given speeds, weight and time... help please???

Question

In 1964, after the 1250-kg jet-powered car Spirit of America lost its parachute and went out of control during a run at Bonneville Salt Flats, Utah, it left skid marks about 8.00 km long. (This earned a place in the Guinness Book of World Records for longest skid marks.)

(a) If the car was moving initially at a speed of about 890 km/h, and was still going at about 350 km/h when it crashed into a brine pond, estimate the coefficient of kinetic friction μk.

_____

(b) What was the kinetic energy of the car 22 s after the skid began?

_____MJ

Answer 1

If we neglect air friction, we can estimate this.

Use the position equation:

S= So + Vo t + 1/2 a t^2

And the velocity equation

V = Vo  + a t

We know So = 0 & Vo = 890 km/h

We also know that at the end of the run, tf (f for final) Sf = 8.0 km, and Vf = 350 km/h

This gives us two equations and two unknowns, t & a/

8.0 km = 0 + 890 km/h * t + 1/2 a t^2

350 km/h = 890km/h + a t

-540 km/h = a t  (solve for a)

-540 km/h /t = a

We can then take a and plug it back into the earlier equation

8.0 km = 890 km/h t + 1/2 (-540 km/h) t  

8.0 km = 620 km/h t

8/620 hr = t or t = 46.45 s

Plug t back in to the equation for a and we get

-540 km/h /t = a

-540 km/h / (8/620)h = -41850 km/h^2 = -3.3 m/s^2

We also know that Ffriction = mu N

Assuming that no mass was lost during the skid, we know that N = 1250 kg * -9.81 m/s^2

Remember that F = m a (newton's first law)

m a = mu N

1250 kg * -3.3 m/s^2 = mu * 1250 kg * -9.81 m/s^2

mu = -3.3 m/s^2 / -9.81 m/s^2

mu = .336

You should be able to determine the velocity using the velocity equation and calculate the Ke usung Ke = 1/2 mv^2