A 1500 kg car skids to a halt on a wet road where μx=0.50...

Key Concepts

Equations of Motion Under Constant Acceleration

Equations of motion under constant acceleration, such as the equation relating velocity and displacement (v² = 2as), provide a method to calculate the initial velocity or deceleration when an object is subjected to a constant force, like friction.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion, expressed as half the product of its mass and the square of its velocity. It is the energy that must be dissipated by friction for an object to stop.

Coefficient of Friction

The coefficient of friction is a dimensionless value that quantifies the interaction between two surfaces. It determines the magnitude of the frictional force when multiplied by the normal force and is crucial in calculating deceleration due to friction.

Friction

Friction is the resistive force that opposes the relative motion between two surfaces in contact. In deceleration scenarios, friction converts the kinetic energy of a moving object into thermal energy, thereby slowing it down.

Work-Energy Principle

The work-energy principle states that the net work done on an object is equal to its change in kinetic energy. This principle is used to connect the energy lost by an object (due to frictional work) to its initial kinetic energy before coming to a halt.

Transcript

00:01 In this question, we're told that a car skids to a halt on a wet road, and we're given the mass as well as the coefficient of friction, and we're asked to find out how fast the car was traveling if it leaves a 65 meter long skid mark.

00:16 So basically what the skid mark part means is that the car was executing its deceleration or its negative acceleration for the 65 meters.

00:27 So ignoring the information, about the coefficient of friction, this at first kind of presents itself as a kinematics question, right? we have a displacement that is 65 meters.

00:45 We have a final speed is zero meters per second because when something is coming to a halt, it is no longer moving, right? but that's kind of where things stop.

00:59 We're asked to find the initial velocity, how fast the car is traveling, but we don't have the acceleration and we don't have the time.

01:08 So that's a bit of a problem in terms of being able to calculate what the initial velocity is.

01:15 Normally we would need to have three givens here, right? so then we can look at either acceleration and time and see if the problem gives us information to calculate one of these.

01:26 Well, yes, it does.

01:28 Because we have some information about the forces.

01:31 We have some information about the friction.

01:34 So we can use that to calculate acceleration.

01:36 So step number one is going to be looking at f -net equals ma and using that to calculate acceleration.

01:46 So if you look at a free body diagram for this car, there's going to be no forward forces.

01:54 So if it's moving towards the right initially, there's going to be no forward forces, there's nothing propelling it forward anymore.

02:01 And all there's going to be is that force of friction between the tires and the road slowing the car down.

02:08 Okay, so the engine's not working anymore.

02:10 It's not doing any, it's not doing any work to push the car forward.

02:15 It's just the friction force slowing it down.

02:17 So the f net, if we take the direction of motion or to the right to be positive, the f net here is going to be negative fk.

02:29 And the mass, you know, we can fill that in later.

02:33 So negative fk is equal to ma, and then we can calculate a by simply dividing this equation by m.

02:42 And so we can use this formula to find a.

02:46 Now, what is fk? well, fk is going to be the coefficient of kinetic friction times the normal force.

02:55 The coefficient of kinetic friction was given to us, so 0.

02:59 And the normal force, since the only two forces in the y direction are the normal force and gravity, the normal force has to equal gravity here.

03:08 So we can substitute m times g for the normal force.

03:14 Now what i'm going to do is i'm going to take that and i'm just going to sub it right back in there.

03:18 If you want to put the numbers in at this point, you absolutely can...

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