Two packages stacked on one another

[hamzaarfeen]

Homework Statement

A delivery van has two packages left that are stacked one on top of another. The upper packages
has a mass of 4.0 kg and is a poorly packaged glass vase, while the lower package has a mass
6.5 kg. The coefficient of static friction between the two packages is 0.211 and the lower box is
fixed to the floor of the van. Since the delivery person is late, he has been accelerating quickly
whenever he has stopped and started (at lights, stop sign etc.), however he never exceeds the
town's speed limit of 60 km/h. What is the minimum amount of time it takes for him to reach
his top speed while still keeping the vase from breaking (sliding off the top box).

Homework Equations

friction= coefficient x contact force
fnet=ma

The Attempt at a Solution

friction = 0.211x 4kg x 9.81
= 8.24N
what do i do next?

 

[_N3WTON_]

a hint: for the 4kg box not to slide off of the 6.5kg box it must have the same acceleration as the 6.5kg box, this acceleration is caused by the static friction between the two boxes

 

[hamzaarfeen]

so how can i solve it? if i make two equations, then one can be made for the upper box using f=ma, but what about the other equation?

 

[_N3WTON_]

so how can i solve it? if i make two equations, then one can be made for the upper box using f=ma, but what about the other equation?

find the acceleration using the hint, and then using this acceleration find the time to reach 60 km/h...I hope I'm not giving away too much but to find the acceleration know that:
$F_{fr top} = (m_{top})(a) = (u_s)(F_{N top})$

 

[HalfLostAndSearching]

To find the minimum amount of time it takes for the delivery person to reach their top speed while keeping the vase from sliding off, we need to use Newton's second law, fnet=ma. The net force acting on the stacked packages is the force of friction between them, which we calculated to be 8.24N. This force is also equal to the mass of the packages (10.5kg) multiplied by their acceleration. So, we can rearrange the equation to solve for acceleration: a = fnet/m = 8.24N/10.5kg = 0.785 m/s^2.

Next, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity (which we can assume to be 0 since the van starts from rest), a is acceleration, and t is time. We know that the town's speed limit is 60 km/h, which is equivalent to 16.67 m/s. So, we can plug in these values and solve for t: t = (16.67 m/s)/0.785 m/s^2 = 21.25 seconds. This is the minimum amount of time it takes for the delivery person to reach their top speed while keeping the vase from sliding off.