A crate is resting on the back of a truck and has a coefficient of of friction of 0.45. What is the maximum acceleration that the truck can undergo before the crate starts to slide off the back of the truck.
µ = f / N, where µ is the coefficient of friction, f is the amount of force that resists motion, and N is the normal force
f=µN
ma=µmg
cancel m on both side:
a=µg
http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/ben_townsend/staticandkineticfriction.htm
THANKS A MILLION. Tutocat.
To find the maximum acceleration at which the crate starts to slide off the back of the truck, we can use the concept of friction.
The maximum acceleration occurs when the force of friction is equal to the maximum static friction, which is given by the equation:
friction force (Ff) = coefficient of friction (μ) * normal force (Fn)
The normal force is equal to the weight of the crate (since it's resting on the back of the truck) and can be calculated using the equation:
normal force (Fn) = mass (m) * gravitational acceleration (g)
Combining these equations, we have:
Ff = μ * m * g
Now, we know that the force experienced by the crate due to acceleration is given by:
force (F) = mass (m) * acceleration (a)
To ensure the crate stays on the truck, the force of friction must be equal to or greater than the force due to acceleration:
μ * m * g ≥ m * a
Simplifying the equation, we find:
a ≤ μ * g
Now, substitute the given coefficient of friction (0.45) and the gravitational acceleration (9.8 m/s^2) into the equation:
a ≤ 0.45 * 9.8
Calculating, we find:
a ≤ 4.41 m/s^2
Therefore, the maximum acceleration that the truck can undergo before the crate starts to slide off the back of the truck is 4.41 m/s^2.