In the figure below, m1 = 10.0 kg and m2 = 4.5 kg. The coefficient of static friction between m1 and the horizontal surface is 0.60, and the coefficient of kinetic friction is 0.30.
m1 is on a table connected to m2 by a string that is on a pulley. m2 is hanging off the table
If the system is set in motion with m2 moving downward, what will be the acceleration of the system?
Why has someone not answered this after over 2 years?
If the system is set in motion with m2 moving downward, what will be the acceleration of the system?
To determine the acceleration of the system, we need to analyze the forces acting on the individual masses.
For m1 on the table:
- There is a gravitational force acting downwards (mg1), where g is the acceleration due to gravity.
- There is a normal force acting upwards (N).
- The force of friction opposing the motion can be either static or kinetic, depending on whether the system is in motion or not.
For m2 hanging off the table:
- There is a gravitational force acting downwards (mg2), where g is the acceleration due to gravity.
- Tension in the string, which is pulling m2 upwards.
Since m2 is moving downward, the tension in the string will be greater than the static friction between m1 and the table. Therefore, the system is in motion, and we will consider the kinetic friction.
Now, let's calculate the force of friction and the net force acting on each mass:
For m1:
The force of friction (Ff) can be calculated using the formula Ff = μN, where μ is the coefficient of kinetic friction and N is the normal force.
The normal force (N) is equal to the weight of m1, N = mg1, where g1 is the acceleration due to gravity.
Therefore, the force of friction on m1 is Ff = μmg1.
The net force on m1 is given by:
Net force on m1 = Tension - Force of friction
Net force on m1 = T - μmg1
For m2:
The net force on m2 is given by:
Net force on m2 = mg2 - T
Now, since the system is connected by a massless string, the tension in the string is the same for both masses. So we can set T equal to each other:
T - μmg1 = mg2 - T
Now we can solve for T:
2T = μmg1 + mg2
T = (μmg1 + mg2) / 2
Now substitute the value of T back into the net force equations:
Net force on m1 = [(μmg1 + mg2) / 2] - μmg1
Net force on m2 = mg2 - [(μmg1 + mg2) / 2]
Next, we can calculate the acceleration (a) of the system using Newton's second law (F = ma):
For m1:
Net force on m1 = m1 * a
For m2:
Net force on m2 = m2 * a
Solve the above equations simultaneously to find the value of acceleration, a.
Please provide the values of m1, m2, μ, g1, and g2 to calculate the acceleration of the system and perform the necessary calculations.