In this problem they show a diagram of a pulley system with an inclined plane (25 degree incline). There is a box called m1=47kg resting on the incline plane and m1=35kg hanging on the vertical line. The question reads: The coefficient of friction between m1 and the surfvace of the inclined plane are Ustatic=0.42 and Ukinetic=0.19.
a)if the masses are held in place and then released , will they start to move? ------> I know the answer is NO.
b)how much mass would you have to add to m2 to cause the masses to begin to move? ----> The answer should be 2.8kg but I don't know how the book got this answer.
c)If you said no to a) and added the mass that you calculated in b), what would be the acceleration of the masses?
ANY help with this problem would be greatly appreciated!! THANK YOU SO MUCH in advance :)
and the answer at the back of this textbook says the acceleration should be 5.7 m/s^2.... but once again.. i don't know how they came up with this answer
well, look at m1. Force down the plane due to gravity: mgSin25
friction opposing motion: mg*mu*cos25
so the force on the m2 side (hanging mass) should be equal to the above sum.
47*9.8(sin25+.42cos25)=35*9.8+addedmass*9.8
your added mass should be the amount it takes to get it started.
Now, acceleration:
Net force= totalmass*a
(35+addedmass)9.8-47*9.8sin25-47*9.8*.19= (35+47+addedmass)a
solve for a.
For the force down the plane due to gravity, why isn't it just F=mg... and thank you so much for your help!
and which u do I use? should I use the static coefficient of friction since it isn't moving yet or the kinetic one since we want to know what will make the masses move?
forget about that last question haha
the formulas you gave didn't give the right answer, or at least not the same answer as they gave in the back of my textbook... any idea why this may be?
for some reason by multiplying the answer that I got for the "mass added" by 35kg, this gave me the answer at the back of the book
still doesn't help with finding the acceleration...
To solve this problem, we will need to consider the forces acting on the system and the conditions necessary for the masses to start moving.
a) To determine if the masses will start to move when released, we need to compare the force due to friction on the inclined plane with the maximum friction force that can be applied. The friction force on the inclined plane is given by:
friction force = (mass on the incline) * (acceleration due to gravity) * (coefficient of friction)
friction force = m1 * g * Ustatic
where m1 is the mass on the incline, g is the acceleration due to gravity, and Ustatic is the coefficient of static friction.
The maximum friction force that can be applied is given by:
maximum friction force = (mass on the incline) * (acceleration due to gravity) * (coefficient of friction)
maximum friction force = m1 * g * Ustatic
If the friction force is less than or equal to the maximum friction force, the masses will remain at rest. However, if the friction force exceeds the maximum friction force, the masses will begin to move.
Substituting the given values:
friction force = (47 kg) * (9.8 m/s^2) * (0.42) = 193.986 N
maximum friction force = (47 kg) * (9.8 m/s^2) * (0.42) = 193.986 N
Since the friction force is equal to the maximum friction force, the masses will not start to move when released. Therefore, the answer to part a) is NO.
b) To determine how much mass needs to be added to mass m2 to cause the masses to begin moving, we need to consider the additional force required to overcome the static friction. In this case, the maximum static friction force is still given by m1 * g * Ustatic.
The force acting down the incline is given by:
force down the incline = (mass on the incline + m2) * g * sin(theta)
where theta is the angle of the incline.
To overcome the static friction force, the force down the incline must be greater than the friction force:
(mass on the incline + m2) * g * sin(theta) > m1 * g * Ustatic
Substituting the given values:
(47 kg + m2) * (9.8 m/s^2) * sin(25 degrees) > (47 kg) * (9.8 m/s^2) * 0.42
Dividing both sides by (9.8 m/s^2) gives:
(47 kg + m2) * sin(25 degrees) > (47 kg) * 0.42
(47 kg + m2) > (47 kg) * 0.42 / sin(25 degrees)
Now we can rearrange the equation to solve for m2:
m2 > (47 kg) * 0.42 / sin(25 degrees) - 47 kg
Plugging in the values and calculating:
m2 > 37.754 kg
So, a minimum of 37.754 kg would need to be added to m2 in order for the masses to start moving. However, since the answer given is 2.8 kg, it appears there may be an error in the book's calculation.
c) If the masses do not start moving and we add the mass calculated in part b) to m2, the system will remain at rest. Therefore, there will be no acceleration of the masses.
In summary:
a) The masses will not start to move when released.
b) To cause the masses to begin moving, a minimum of 37.754 kg needs to be added to m2.
c) If the masses do not start moving and the calculated mass is added to m2, there will be no acceleration of the masses.