Friction and Acceleration: Solving for the Motion of a Moving Sculpture

AI Thread Summary
The discussion revolves around calculating the motion of a Dale Chihouly glass sculpture being transported in a van, focusing on its potential to slide due to acceleration. The sculpture, initially at rest, is subjected to a force as the van accelerates, which must be analyzed using static and kinetic friction coefficients. The acceleration of the van is determined to be 2.5 m/s², which is essential for assessing the forces acting on the sculpture. The participants emphasize the need to compare the net force on the sculpture with the maximum static friction force to establish whether it will slide. Ultimately, the problem requires calculating the time it takes for the sculpture to slide 3.0 meters and its speed upon collision with the back wall of the van.
Blueice781
Messages
1
Reaction score
0

Homework Statement


You are transporting a $150,000 Dale Chihouly glass sculpture in your van. You stop at a hotel, where they have a valet parking. The valet gladly takes the wheel of your car and covers 20 meters from rest in 2.00 seconds. Between the sculpture and the floor of you van, mustatic=1.00 and mukinetic=.60, the sculpture is 3.00 meters from the back of the van.
a. Prove that the sculpture will start sliding towards the back of the van.
b. How long will it take the sculpture to accelerate from rest to slide 3.0 meters and smash into the back wall of the van?
c. How fast will the sculpture be going as it collides with the back of the van?


Homework Equations


2ax=v2-vo2
There might be more, but I don't know.

The Attempt at a Solution


a. 2a(20)=102-0
a=2.5m/s2
 
Physics news on Phys.org
Welcome to PF!

If you are given position and time and asked to work out acceleration you are better off using a different kinematic equation. I don't see the question telling me the final velocity is 10m/s anywhere. Once you have the acceleration of the van, compare the amount of force on the sculpture with the maximum static friction force.
 
fnet = ma

you need to figure out your acceleration, then prove with a static equation that you have enough fnet to overcome mu static. Then use mu kinetic to determine the acceleration of the sculpture relative to the van. I don't remember the equations right off hand, but with a couple of equations it won't be too hard.
 
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top