You are driving at a reasonable constant velocity in a van with a windshield tilted 120o relative to the horizontal. As you pass under a utility worker fixing a power line, the worker’s wallet falls onto the windshield. Determine the acceleration needed by the van so that the wallet stays in place if frictional forces are negligible.
The situation is represented in the free-body diagram attached to this answer.
We see that there are only two forces acting on the wallet:
- The force of gravity, downward, of magnitude , where m is the mass of the wallet and g is the acceleration due to gravity
- The normal reaction of the windshield on the wallet, N, in the direction perpendicular to the windshield
Resolving the normal reaction into the two directions - horizontal and vertical - the two equations of motion are:
is the angle between the horizontal and the normal reaction
is the horizontal acceleration of the van
We can rewrite eq.(1) as
And dividing by eq(2),
And solving for a, we find the acceleration of the van:
The vectors are broken into components in orthogonal directions.The orthogonal vector components are treated independently of each other.
The acceleration of van is a= 11 m/s ²
We can solve this problem based on its accelerations , The acceleration due to gravity will have two components relative to the windshield, parallel and perpendicular, given by
g║= g sin θ
g⊥ = g cosθ
The acceleration due to van will also have same two components , but the acceleration is along the horizontal, than vertical the trig functions will be opposite what they were for gravity.
a║= a cos θ
a⊥= a sin θ
To isolate the van's acceleration
a= g sin (θ) ± μs cos (θ) / cos (θ) ± μs sin (θ)
θ = 180°- 120°
We can assume that van is not decelerating with 30 g's and giving the acceleration of the van as
a= 11 m/s²
no simpler subs form complex ones. synthesise = make
we need to know the time interval during which the force acts. impulse of force = momentum change