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Moment of Inertia and Translational Motion

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1. A four-wheel truck that has a mass of 5,000 kg accelerates forward. The coefficient of friction for the front and back wheels is 0.2 and 0.4, respectively. What is the acceleration of the truck? Assume that the friction force on both the front and rear wheels are at a maximum and both are about to slip.

2. Each of the 2 blocks A and B weigh 32.2 lb. A small strip is nailed onto the top surface of B to prevent A from sliding while the force P accelerates the system on a smooth plane. Determine the maximum value of P without causing A to tip? (Assume ground is frictionless.)

3. A 1800 kg 4-wheel car has its back wheels stuck in mud. Although the back tires slip, the front tires rotate without slipping. What is the car's acceleration if C is the center of mass, and u_k = 0.3 for the front tires?

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1.)
mu1 = 0.4
mu2 = 0.2
m = 5000 kg
g = 9.8 m/s^2

In vertical direction:
R1 + R2 = 0 .......(1)

in horizontal direction:
f1 + f2 = m*a
=> mu1*R1 + mu2*R2 = m*a ..........(2)

Pseudo force Fp = m*a (backward)

Moment about the front wheel,
-R1*5 + m*g*3 + m*a*1 = 0 ........(3)

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