A 2600 kg truck traveling at 72 km/h slams on the brakes and skids to a stop. The frictional
force between the truck and the road is 8200 N. Calculate the mechanical work required to stop
the truck and the distance the truck travels before stops.
Idk
To calculate the mechanical work required to stop the truck, we can use the formula:
Work = Force x Distance
First, let's convert the speed from km/h to m/s:
72 km/h = 72,000 m/60 s = 1,200 m/s
Next, we need to determine the deceleration (negative acceleration) of the truck.
Using Newton's second law of motion,
Force = Mass x Acceleration
Rearranging the equation, we can calculate the acceleration:
Acceleration = Force / Mass
Acceleration = 8200 N / 2600 kg = 3.15 m/s^2
Now, we can calculate the time it takes for the truck to stop using the acceleration and initial speed:
v = u + at
0 = 1,200 m/s + (-3.15 m/s^2) x t
Solving for t gives us:
t = -1,200 m/s / -3.15 m/s^2 = 381.0 s
Finally, we can calculate the distance traveled using the equation:
Distance = Initial velocity x Time + 0.5 x Acceleration x Time^2
Distance = 1,200 m/s x 381.0 s + 0.5 x (-3.15 m/s^2) x (381.0 s)^2
Therefore, the distance the truck travels before stopping is approximately equal to 228,494.5 meters (or 228.5 km).
Now that we have the distance, we can calculate the mechanical work required to stop the truck:
Work = Force x Distance
Work = 8200 N x 228,494.5 m
Therefore, the mechanical work required to stop the truck is approximately equal to 1,873,548,900 Joules.
To calculate the mechanical work required to stop the truck, we need to use the formula for work:
Work = Force x Distance
In this case, the force acting on the truck is the frictional force between the truck and the road, which is 8200 N. We also need to find the distance traveled by the truck before it comes to a stop.
The first step is to convert the speed of the truck from km/h to m/s, since the frictional force and mass are given in standard SI units.
To convert km/h to m/s, we need to divide the speed by 3.6 (since there are 3.6 seconds in an hour and 1000 meters in a kilometer).
So, the speed of the truck in m/s is 72 km/h / 3.6 = 20 m/s.
Now we can calculate the distance traveled by the truck using the formula:
Distance = (Initial Velocity^2) / (2 * Acceleration)
Since the truck comes to a stop, its final velocity is 0. Therefore, the acceleration can be calculated using the equation:
Acceleration = (Final Velocity^2 - Initial Velocity^2) / (2 * Distance)
Plugging in the values, we get:
Acceleration = (0 - 20^2) / (2 * Distance)
Acceleration = 400 / (2 * Distance)
Acceleration = 200 / Distance
Now we can plug the acceleration value into Newton's second law of motion to find the frictional force:
Force = Mass x Acceleration
8200 N = 2600 kg x (200 / Distance)
Distance = 2600 kg x (200 / 8200 N)
Solving this equation, we find that the distance the truck travels before stopping is approximately 63.41 meters.
Finally, we can calculate the work required to stop the truck using the formula mentioned earlier:
Work = Force x Distance
Work = 8200 N x 63.41 m
Therefore, the mechanical work required to stop the truck is approximately 531,610 Joules.
work must equal 1/2 m v^2 change v to m/s.
then 8200*distance= work above, calculate distance to stop