Determine the force required to bring an 8-ton truck traveling at 50 mph to rest in 5 seconds. How far does it travel?
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First, we need to convert the weight of the truck from tons to kilograms and the speed from mph to m/s.
1 ton = 907.185 kg
So, 8 tons = 8 * 907.185 = 7257.48 kg
1 mph = 0.44704 m/s
So, 50 mph = 50 * 0.44704 = 22.352 m/s
We can use Newton's second law of motion (F = ma) to find the force required to stop the truck.
First, we need to find the acceleration (a). Acceleration is the change in velocity divided by the time it takes for the change to occur. In this case, the truck is going from 22.352 m/s to 0 m/s in 5 seconds.
a = (v_f - v_i) / t
a = (0 - 22.352) / 5 = -4.4704 m/s^2
The negative sign indicates that this is deceleration, or acceleration in the opposite direction of motion.
Now we can find the force (F):
F = m * a
F = 7257.48 kg * -4.4704 m/s^2 = -32444.8 N
The negative sign indicates that the force is acting in the opposite direction of the truck's motion, which makes sense because we're trying to stop the truck.
So, the force required to stop the truck is 32444.8 N.
To find the distance the truck travels, we can use the equation for motion:
d = v_i * t + 0.5 * a * t^2
d = 22.352 m/s * 5 s + 0.5 * -4.4704 m/s^2 * (5 s)^2
d = 111.76 m - 55.88 m = 55.88 m
So, the truck travels approximately 55.88 meters before coming to a stop.