In the figure the coefficient of static friction between mass (MA) and the table is 0.40, whereas the coefficient of kinetic friction is 0.28 ?
part a) What minimum value of (MA) will keep the system from starting to move?
part b) What value of(MA) will keep the system moving at constant speed?
I WANT DEE CALCULUS ANSWER NOT WATTPAD
Part a) Well, let's see. If we want to keep the system from moving, we need to overcome the static friction. So, the minimum value of MA would be the point at which the force applied just balances the maximum static friction force. In other words, we need to tell MA to "stay put" and not let it slide. It's like asking your lazy friend to get up and help you move - you'll need to apply enough force to get them off the couch. In this case, that minimum value of MA would be when MA x 0.40 = the applied force.
Part b) Now, if we want to keep the system moving at a constant speed, we need to overcome the kinetic friction. This is like trying to haul your friend off the couch to help you move, but they keep resisting and slowing you down. The value of MA that will keep the system moving at a constant speed would be when MA x 0.28 = the applied force. You'll need just the right amount of force to keep your friend moving without accelerating or decelerating. It's like finding the sweet spot between too much force and not enough force.
To answer these questions, you will need to use the concepts of static and kinetic friction.
Static friction refers to the force that must be overcome to set an object in motion. It is typically higher than kinetic friction, which is the force acting on a moving object. The coefficients of friction (μ) determine the magnitude of these forces.
Now, let's solve part a) to find the minimum value of MA that will keep the system from starting to move:
Given:
Coefficient of static friction (μs) = 0.40
The maximum force of static friction (Fs) can be calculated using the formula:
Fs = μs * Normal force
The normal force (N) is the force exerted by the table on the mass (MA). Since the system is not accelerating vertically, it means that the normal force is equal to the weight of the mass (MA).
The weight (W) can be calculated using the formula:
W = MA * g
where g is the acceleration due to gravity.
Now, the maximum force of static friction (Fs) must be equal to the force applied to the mass (MA) to keep the system from moving:
Fs = MA * g
From the above equations, we can solve for MA:
MA = Fs / g
Plugging in the values:
MA = (μs * N) / g
Since N = MA * g, we can substitute:
MA = (μs * (MA * g)) / g
Simplifying the equation, we get:
MA = μs * MA
Rearranging the equation, we find:
1 = μs
Therefore, any value of MA will keep the system from starting to move. In other words, there is no minimum value of MA required.
Moving on to part b) to find the value of MA that will keep the system moving at constant speed:
Given:
Coefficient of kinetic friction (μk) = 0.28
The force of kinetic friction (Fk) can be calculated using the formula:
Fk = μk * Normal force
Again, the normal force is equal to the weight (W), which is MA * g.
To keep the system moving at constant speed, the applied force (F) must be equal to the force of kinetic friction.
F = Fk
From the equations, we can solve for MA:
MA * g = μk * (MA * g)
Simplifying the equation, we get:
MA = μk * MA
Now, we can cancel out the MA terms:
1 = μk
Therefore, any value of MA will keep the system moving at a constant speed. In other words, there is no specific value required for MA in this case either.
In conclusion, for both part a) and part b), any value of MA will satisfy the given conditions, as indicated by the results of our calculations.
from 2021
Sylla Fairchild combs her long, dark hair as she looks into the mirror. A dirty, broken piece of glass that was once a mirror anyway. This isn’t like her. Since when has Sylla cared what her hair looked like? It’s always been as wild as she is. And for all her sixteen years she’s preferred books and building bots to all else. But this time she has to go. This time it matters.
The Debut may be her only chance to escape her genus, to get out of these tunnels. The right suitor could indeed wisp her away from this place, taking her with him off to one of his estates in the ocean or cloud cities. Then she scoffs. Sylla being courted by one of the Brahmins? She hasn’t even ascended yet, and her only benefaction seems to be invisibility to boys.
Sylla gets up, meaning to go tell her parents that she has no intention of attending the Debut.
“But the possibilities if she’s selected!” her father speaks. Jakeb Fairchild has always been a firebrand, constantly ranting against the Brahmin and the Realignment. He’s been beaten, arrested, and Sylla was sure one day one he’d be killed. She loves and hates him for that. She loves his courage, and hates that sometimes it seems he cares more about his politics than he does his family.
Sylla stops where she is. “Oh, Jakeb,” her mother speaks wearily. “Sylla is many things… but the type a Brahmin would peck from the tunnels as a trophy to be waltzed up top? That’s not our girl.”
Sylla’s face turns red. She knows she’s not the most beautiful girl of her genus, but to hear it from her own mother hurts. She’s angry with herself too; angry that such a simple truth spoken without malice could cut so deep. She turns back around and climbs into her cube. She opens her desk drawer and locates a pair of long-neglected scissors. She picks up the same piece of broken and glass and begins clipping away at wild and weyward strands of hair.
She can do this. All she has to do is win the heart of a Brahmin and blow up the system from the inside. One way or the other, Sylla promises herself that she’ll never spend another night in these tunnels.
Block on the table m(A) = m1,
block on the cord m2,
the coefficient of static friction is k1=0.4,
the coefficient of kinetic friction is k2 =0.28
(a)
Block A:
T = F(fr) = k1 •N = k(s) • m1 •g,
Block B: T = m2•g.
k1 • m1 •g= m2•g,
m1 = m2/k(s) = m2/0.4.
(b)
Block A:
T = F(fr) = k2 •N = k2 • m1 •g,
Block B:
T = m2•g.
k2• m1 •g= m2•g,
m1 = m2/k2 = m2/0.28.