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Answer :
Final answer:
To find the maximum shearing force in the pegs during the truck's acceleration, Newton's second law is applied, and the weight and acceleration of the gate are considered. The final shear force for each peg is 7.7021 lbs.
Explanation:
To find the maximum shearing force in each peg during the acceleration of the pickup truck with the trailer, we need to apply Newton's second law.
First, let's convert the speed from miles per hour to feet per second (1 mi/hr = 1.46667 ft/s):
37 mi/hr × 1.46667 ft/s/mi/hr = 54.2667 ft/s
Using the kinematic equation v^2 = u^2 + 2as (where v is final velocity, u is initial velocity, s is distance, and a is acceleration), we can solve for acceleration (a) since the truck starts from rest (u = 0):
54.2667^2 = 0 + 2 × a × 215
a = × 54.2667^2 / (2 × 215) = 6.88776 ft/s^2
The force affecting the gate pegs comes from the horizontal component of the gravitational force and the force due to acceleration. Assume that the mass of the gate is 72 lbs; the gravitational force is:
F_gravity = m × g = 72 lbs (Since g in lbs already accounts for Earth's gravitational acceleration)
To find the force due to acceleration, we use F = m × a:
F_acceleration = 72 lbs × 6.88776 ft/s^2
However, since lbs already include g, we convert lbs to mass in slugs:
m = 72 lbs / 32.2 ft/s^2 = 2.23602 slugs
F_acceleration = 2.23602 slugs × 6.88776 ft/s^2 = 15.4042 lbs
The total force on each peg is thus the shearing force due to the acceleration, but as there are two pegs, we divide the total force by 2, assuming the load is distributed evenly:
Shear force per peg = F_acceleration / 2 = 15.4042 lbs / 2 = 7.7021 lbs (rounded to four significant figures)
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