During the investigation of a traffic accident, police find skid marks 31 meters long. They determine the coefficient of kinetic friction between the car's tires and the roadway to be 0.515 for the prevailing conditions. What was the speed of the car when its brakes were applied? Hint: Either pick a mass for the car or work in terms of variables.
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It's easier to pick a mass. 1kg. works well. Weight = 9.8N.
(9.8 x 0.515) = braking force of 5.047N.
Acceleration = (f/m) = 5.047/1, = 5.047m/sec^2.
Velocity = sqrt.(2ad), = 17.69m/sec.
(9.8 x 0.515) = braking force of 5.047N.
Acceleration = (f/m) = 5.047/1, = 5.047m/sec^2.
Velocity = sqrt.(2ad), = 17.69m/sec.
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Hello,
What suvat variables do we know for acceleration?
s = 31 m
v = o m/s after car has stopped.
and we need acceleration ..... not enough known, but we can write an equation for initial velocity and acceleration
v^2 = u^2 + 2as
0 = u^2 + 2as
u^2 = - 2as
u = sqrt (-2as)
We also know that sum of the forces (F) = m * a, so a = F/m,
and F = friction force = Normal force * coefficeint of friction = N * U
and N = mass * gravity = mg
so F = N * U = m * g * U
and a = F / m = m * g * U / m = U * g
plug that into our other equation
u = sqrt ( - 2 * U * g * s)
u = sqrt ( - 2 * 0.515 * - 9.81 m/s^2 * 31 m)
u = 17.7 m/s
Good Luck
EDIT -- Yes, you can pick a mass for the car, the question says it's ok. That's the BABY way, however. You wanna do stuff the baby way? Or put on your big boy pants and do it properly. Notice how the other answer stops to crank out all kinds of useless numbers that only increase your round off error. He calculated that a 1 kg car would weigh 9.8 N. Wow. And that a 1 kg car would have a certain braking force. Useless, who cares about the braking force of a hypothetical 1 kg car? then he calculates the acceleration. Great. Not asked for or needed.
A big boy would work all in variables and only plug in the numbers at the end, only use the calculator ONCE. A baby does the "plug and chug". If you ever advance in the science or engineering you will not have time for all the wasted calculator manipulation during examinations. Get used to working all in variables whenever possible. That's why you spent a few years studying ALGEBRA, so you could flip equations around like a circus juggler. Not take one baby step and fart out a number, take another baby step and fart out another number.....ad infinitum
If you wanna be really good, you should attempt to keep your solutions in all variables until your final equation. And sometimes most of the variables will cancel each other out, you are left with one simple solution while all the plug and chuggers are cranking out all these numbers at every single step along the way. If you can master this technique, you will be streets ahead of the others.
The ultimate goal is to have (on the left side of your equation) only what the question asked for and (on the right side) only the variables expressly given in the question. Like here, they asked for initial speed and give you distance and coefficient of friction. In my equation you put in the coefficient, the distance and gravity and you get initial velocity.
What suvat variables do we know for acceleration?
s = 31 m
v = o m/s after car has stopped.
and we need acceleration ..... not enough known, but we can write an equation for initial velocity and acceleration
v^2 = u^2 + 2as
0 = u^2 + 2as
u^2 = - 2as
u = sqrt (-2as)
We also know that sum of the forces (F) = m * a, so a = F/m,
and F = friction force = Normal force * coefficeint of friction = N * U
and N = mass * gravity = mg
so F = N * U = m * g * U
and a = F / m = m * g * U / m = U * g
plug that into our other equation
u = sqrt ( - 2 * U * g * s)
u = sqrt ( - 2 * 0.515 * - 9.81 m/s^2 * 31 m)
u = 17.7 m/s
Good Luck
EDIT -- Yes, you can pick a mass for the car, the question says it's ok. That's the BABY way, however. You wanna do stuff the baby way? Or put on your big boy pants and do it properly. Notice how the other answer stops to crank out all kinds of useless numbers that only increase your round off error. He calculated that a 1 kg car would weigh 9.8 N. Wow. And that a 1 kg car would have a certain braking force. Useless, who cares about the braking force of a hypothetical 1 kg car? then he calculates the acceleration. Great. Not asked for or needed.
A big boy would work all in variables and only plug in the numbers at the end, only use the calculator ONCE. A baby does the "plug and chug". If you ever advance in the science or engineering you will not have time for all the wasted calculator manipulation during examinations. Get used to working all in variables whenever possible. That's why you spent a few years studying ALGEBRA, so you could flip equations around like a circus juggler. Not take one baby step and fart out a number, take another baby step and fart out another number.....ad infinitum
If you wanna be really good, you should attempt to keep your solutions in all variables until your final equation. And sometimes most of the variables will cancel each other out, you are left with one simple solution while all the plug and chuggers are cranking out all these numbers at every single step along the way. If you can master this technique, you will be streets ahead of the others.
The ultimate goal is to have (on the left side of your equation) only what the question asked for and (on the right side) only the variables expressly given in the question. Like here, they asked for initial speed and give you distance and coefficient of friction. In my equation you put in the coefficient, the distance and gravity and you get initial velocity.