A flatbed egg truck is in a drag race. The truck is carrying a 450 lb. crate of eggs in the back. The coefficients of friction between the crate and the truck bed are μs = 0.9 and μk = 0.4. What is the maximum acceleration the truck can have without the eggs sliding off the back of the truck?

1) 3.9 m/s2
2) 8.8 m/s2
3) 24 m/s2
4) 180 m/s2
5) 400 m/s2

2) 8.8 m/s2

m•a=F(fr)=μ(s) •m•g
a= μ(s) • g

To find the maximum acceleration the truck can have without the eggs sliding off the back of the truck, we need to determine the maximum value of the static friction force acting on the eggs.

The maximum static friction force (Fs) can be calculated using the equation: Fs = μs * N

Where:
- Fs is the maximum static friction force
- μs is the coefficient of static friction
- N is the normal force

The normal force (N) is equal to the weight of the crate, which is 450 lb. We need to convert it to Newtons, so we can use the equation: 1 lb = 4.45 N.

N = 450 lb * 4.45 N/lb = 2002.5 N

Now we can calculate the maximum static friction force:

Fs = 0.9 * 2002.5 N = 1802.25 N

The maximum static friction force is equal to the net force acting on the eggs in the horizontal direction, which is equal to the product of the mass of the eggs (m) and the maximum acceleration (a). The mass (m) can be calculated using the equation: F = m * a

The force (F) is equal to the maximum static friction force (Fs).

Fs = m * a

Rearranging the equation, we can solve for the maximum acceleration (a):

a = Fs / m

To calculate the mass (m) of the eggs, we need to use the equation: F = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).

F = 450 lb * 4.45 N/lb = 2002.5 N

2002.5 N = m * 9.8 m/s^2

m = 2002.5 N / 9.8 m/s^2 = 204.59 kg

Now, we can calculate the maximum acceleration (a):

a = Fs / m = 1802.25 N / 204.59 kg ≈ 8.819 m/s^2

Therefore, the maximum acceleration the truck can have without the eggs sliding off the back of the truck is approximately 8.819 m/s^2. Therefore, the answer is option 2) 8.8 m/s^2.