Consider the system shown, Block A weighs 45N and block b weighs 25N. Once block b is set into downward motion, it descends at a constant speed.
Its an atwood machine with A resting on a surface and B dangling off the surface.
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B
uk equals 0.556 i got that
If the weight of block B is doubled, find the acceleration .
Use this equation the sum of the forces in the system= Mass of system* Acceleration of system to find acceleration.
Whats the driving and resistance force and whyd you choose that?
the pulling force Mb*acceleratin minus the friction force = (total mass)a
or
B/g*a - A/g*9.8*.556=(Ma+Ma)*a
so this converts the given weights of the masses to masses as
B/g = MassB and A/g= MassA
so solve for acceleration a.
In the given Atwood machine system, when block B is set into downward motion and descends at a constant speed, the driving force is the force exerted by block A pulling block B downwards, and the resistance force is the force of friction acting on block B, which opposes its motion.
To determine the acceleration of the system when the weight of block B is doubled, we can use the equation:
Sum of the forces in the system = Mass of the system * Acceleration of the system
The sum of the forces in the system can be calculated as follows:
Sum of the forces = Driving force - Resistance force
The driving force can be determined by considering that block A exerts a force equal to its weight, which is given as 45N:
Driving force = Weight of block A = 45N
The resistance force is the force of friction acting on block B, which can be calculated using the equation:
Resistance force = coefficient of kinetic friction * Normal force
In this case, the normal force is equal to the weight of block B, as block B is resting on a surface and is not accelerating vertically:
Normal force = Weight of block B = 25N
Given that the coefficient of kinetic friction is 0.556, the resistance force can be calculated as:
Resistance force = 0.556 * 25N = 13.9N
Substituting the driving force and the resistance force into the equation for the sum of the forces, we get:
Sum of the forces = 45N - 13.9N = 31.1N
Finally, we can use the sum of the forces and the mass of the system to find the acceleration:
Sum of the forces = Mass of the system * Acceleration of the system
Rearranging the equation to solve for acceleration, we have:
Acceleration of the system = Sum of the forces / Mass of the system
To find the new acceleration when the weight of block B is doubled, we need to know the mass of the system. The mass of the system can be calculated by summing the masses of block A and block B.
Assuming the acceleration due to gravity is 9.8 m/s², let's calculate the mass of the system:
Mass of block A = Weight of block A / acceleration due to gravity = 45N / 9.8 m/s²
Mass of block B = Weight of block B / acceleration due to gravity = 25N / 9.8 m/s²
Now, we can calculate the total mass of the system:
Mass of the system = Mass of block A + Mass of block B
Substituting the known values and solving for the total mass, we can then find the new acceleration using the equation:
Acceleration of the system = Sum of the forces / Mass of the system
Now, let's calculate the values step by step.
In this system, block A is resting on a surface and block B is hanging off the surface. When block B is set into downward motion, it descends at a constant speed. To find the acceleration when the weight of block B is doubled, we can use the equation for the sum of the forces in the system.
In an Atwood machine, the driving force is usually provided by the difference in weights of the two blocks. In this case, the driving force is the weight of block A minus the weight of block B, since block A is resting on a surface. So, the driving force is:
Driving Force = Weight of block A - Weight of block B
The resistance force, on the other hand, is the friction force opposing the motion of the system. In this case, the given value of 0.556 represents the coefficient of kinetic friction (uk) between block A and the surface it rests on. The resistance force can be calculated by multiplying the normal force (weight of block A) by the coefficient of kinetic friction. Therefore, the resistance force is:
Resistance Force = Coefficient of Kinetic Friction * Weight of block A
Now that we have identified the driving force and the resistance force, we can use the equation:
Sum of Forces in the System = Mass of the System * Acceleration of the System
Substituting the driving force and the resistance force into the equation gives:
(Driving Force - Resistance Force) = (Mass of block A + Mass of block B) * Acceleration
In this case, when the weight of block B is doubled, the driving force becomes:
New Driving Force = Weight of block A - (2 * Weight of block B)
Using this new driving force, we can solve the equation to find the acceleration of the system.