A loaded tractor-trailer with a total mass of 5000 kg traveling at 3.0 km/h hits a loading dock and comes to a stop in 0.64 s. What is the magnitude of the average force exerted on the truck by the dock?
3km/hr=3km/hr*1hr/3600sec*1000m/1km=0.83m/s
force*time=mass*changevelociyt
force= 5000*.83/.64 N = ???
To find the magnitude of the average force exerted on the truck by the dock, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's convert the speed of the truck from km/h to m/s. Since 1 km/h is equal to 0.2778 m/s, we can calculate:
Speed (v) = 3.0 km/h * 0.2778 m/s = 0.8334 m/s
Now, let's calculate the acceleration of the truck using the formula:
Acceleration (a) = Change in velocity / Time taken
Acceleration (a) = Final velocity (0 m/s) - Initial velocity (0.8334 m/s) / Time (0.64 s)
Since the truck comes to a stop, the final velocity is 0 m/s. Therefore:
Acceleration (a) = -0.8334 m/s / 0.64 s = -1.3016 m/s²
Now, we can calculate the force using Newton's second law:
Force (F) = Mass (m) * Acceleration (a)
Force (F) = 5000 kg * -1.3016 m/s² = -6508 N
The magnitude of the force exerted on the truck by the dock is the absolute value of the force, which is:
Magnitude of Force = | -6508 N | = 6508 N
Therefore, the magnitude of the average force exerted on the truck by the dock is 6508 Newtons.
To find the magnitude of the average force exerted on the truck by the dock, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, we need to determine the acceleration of the truck. We know that the truck comes to a stop, so its final velocity is 0. We also know that the initial velocity is given in kilometers per hour, so we need to convert it to meters per second:
Initial velocity (v_i) = 3.0 km/h
To convert km/h to m/s, we can use the conversion factor: 1 km/h = 0.2778 m/s.
Therefore, v_i = 3.0 km/h * 0.2778 m/s = 0.8334 m/s (rounded to four decimal places).
Next, we can calculate the acceleration (a) by using the equation:
v_f = v_i + a * t
Since the final velocity is 0, we can rearrange the equation to solve for acceleration:
a = (v_f - v_i)/t
Plugging in the values, we get:
a = (0 - 0.8334 m/s) / 0.64 s ≈ -1.302 m/s^2
(Note: The negative sign indicates that the truck is decelerating or experiencing a negative acceleration.)
Now, we can calculate the magnitude of the average force using Newton's second law:
F = m * a
Plugging in the values, we get:
F = 5000 kg * (-1.302 m/s^2) ≈ -6510 N
The magnitude of the average force exerted on the truck by the dock is approximately 6510 N.