A flatbed truck is carrying a 2540 kg crate of heavy machinery. If the coefficient of static friction between the crate and the bed of the truck is 0.540 , what is the maximum rate (in meters/second^2) that the driver can decelerate when coming to a stop, in order to avoid crushing the cab of the truck with the crate?
M*a = Max static friction force
= M*g*0.54
M cancels out
a = 0.54g = 5.29 m/s^2
(assuming the crate is not tied down)
To determine the maximum rate at which the driver can decelerate, we need to consider the static friction force between the crate and the truck bed. This friction force is what prevents the crate from sliding forward and crushing the cab of the truck.
The formula to calculate the maximum static friction force is given by:
F_max = μ_s * N
where:
F_max is the maximum static friction force,
μ_s is the coefficient of static friction,
N is the normal force.
In this case, the normal force N is equal to the weight of the crate, since the crate is resting on the truck bed. The weight of an object can be calculated using the equation:
Weight = mass * acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2.
Weight = 2540 kg * 9.8 m/s^2
Now, let's calculate the normal force N:
N = Weight = 2540 kg * 9.8 m/s^2
Next, we can determine the maximum static friction force F_max:
F_max = μ_s * N = 0.540 * (2540 kg * 9.8 m/s^2)
Finally, to find the maximum deceleration rate, we equate the maximum static friction force to the product of the mass of the crate and the deceleration rate:
F_max = mass * deceleration rate
By rearranging the equation, we can solve for the deceleration rate:
deceleration rate = F_max / mass
deceleration rate = (0.540 * (2540 kg * 9.8 m/s^2)) / 2540 kg
Now, we can calculate the deceleration rate:
deceleration rate = (0.540 * (2540 kg * 9.8 m/s^2)) / 2540 kg
Therefore, the maximum rate at which the driver can decelerate is equal to the calculated deceleration rate.