A rope is attached from a truck to a 1403 kg car. The rope will break if the tension is greater than 2375 N. Neglecting friction, what is the maximum possible acceleration of the truck if the rope does not break?
m/s2
If the truck can reach 30 mph within 7.5 s, should the driver of the truck be concerned that the rope might break?
To find the maximum possible acceleration of the truck without breaking the rope, we need to calculate the tension in the rope when the car is subjected to the maximum acceleration.
We can start by calculating the force applied to the car:
Force = mass * acceleration
Given:
Mass of the car (m) = 1403 kg
Now, let's find the maximum acceleration:
Force = 2375 N (the maximum tension the rope can handle)
2375 N = 1403 kg * acceleration
Solving for acceleration:
acceleration = 2375 N / 1403 kg
acceleration ≈ 1.693 m/s^2
Therefore, the maximum possible acceleration of the truck without breaking the rope is approximately 1.693 m/s^2.
Now, let's determine if the driver should be concerned that the rope might break given that the truck can reach 30 mph within 7.5 seconds.
First, let's convert 30 mph to meters per second (m/s):
30 mph = 13.4112 m/s (approximately)
The acceleration of the truck can be calculated using the formula:
acceleration = (final velocity - initial velocity) / time
Given:
Final velocity (v) = 13.4112 m/s
Initial velocity (u) = 0 m/s
Time (t) = 7.5 s
acceleration = (13.4112 m/s - 0 m/s) / 7.5 s
acceleration ≈ 1.7882 m/s^2
Comparing this acceleration (1.7882 m/s^2) with the maximum possible acceleration without breaking the rope (1.693 m/s^2), we can see that the acceleration is within the limit. Therefore, the driver of the truck should not be concerned that the rope might break.