Question

A crate of mass 43 kg is loaded onto the back of a flatbed truck. The coefficient of static friction between the box and the truck bed is 0.47. What is the maximum acceleration a (in m/s2) the truck can have without the crate sliding off?

Answer 1

Draw a picture and label the forces to better understand the question.

Sum the forces in the x direction since its asking for acceleration (motion is usually in x direction so you're being asked to find a_x (x- axis).

Sum of F_x = ma_x

The only force on x axis is static friction (mu_s) pointing toward the box in a direction that will keep it from sliding as the truck moves.

so,

mu_s = ma_x

we know that mu*N = static friction

so solve for normal force by summing forces on Y axis = N - mg =0 (no acceleration on Y axis)

N = mg

Finally,

mu_S (mg) = ma_x

solve for a_x. notice that masses cancel

thus:

mu_S*g = a_x

Final answer: 4.61

Hope that wasn't too confusing. If you can draw/label the diagram properly you can solve it properly too! :)