A 5200 kg truck, moving forward at 70.0 km/h, has its brakes applied and comes to restover a distance of 45.0 m. Determine the resistive force on the truck (due to friction andair resistance).
Question
A 5200 kg truck, moving forward at 70.0 km/h, has its brakes applied and comes to restover a distance of 45.0 m. Determine the resistive force on the truck (due to friction andair resistance).
Solution
To solve this problem, we need to use the principles of physics, specifically Newton's second law of motion and the equations of motion. Here are the steps:
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Convert the speed from km/h to m/s: 70 km/h = 70,000 m/3600 s = 19.44 m/s.
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Use the equation of motion v^2 = u^2 + 2as to find the acceleration (a). Here, v is the final velocity (0 m/s, since the truck comes to rest), u is the initial velocity (19.44 m/s), and s is the distance (45 m). Solving for a gives us:
0 = (19.44 m/s)^2 + 2a45 m => a = -(19.44 m/s)^2 / (2*45 m) = -4.21 m/s^2
The negative sign indicates that this is a deceleration.
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Use Newton's second law F = ma to find the resistive force (F). Here, m is the mass of the truck (5200 kg) and a is the acceleration (-4.21 m/s^2). Solving for F gives us:
F = 5200 kg * -4.21 m/s^2 = -21892 N
The negative sign indicates that the force is acting in the opposite direction to the motion of the truck, which is what we expect for a resistive force.
So, the resistive force on the truck due to friction and air resistance is 21892 N.
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