A force of 23.52 N pushes and pulls to blocks
as shown in the figure below. The vertical
contact surfaces between the two blocks are
frictionless. The contact between the blocks
and the horizontal surface has a coefficient of
friction of 0.29.
The acceleration of gravity is 9.8 m/s2
What is the magnitude a of the acceleration
of the blocks?
Answer in units of m/s2
You need to include the referenced figure or fully detail it with text.
How do I do that?
the only info missing is the angle is 60 degrees...
force >
=> block1 block2 /
force @60deg
uk=0.29
assuming the force is at some angle downward. Figure the horizontal, and vertical (downward components) The horizontal force is the pushing force, opposing friction and inertial.
The friction is mu*mg on each block, but on whichever block that there is a downward component of force, it adds to mg to increase friction. So figure friction.
Net force=m*a
forcehorizontal-forcefriction=ma
We need the mass of each block. We also need to know exactly what you mean by 60 degrees. Is that 60 degrees from vertical, or 60 degrees from horizontal?
To find the magnitude of the acceleration (a) of the blocks, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. In this case, the force is the net force acting on the blocks.
First, we need to determine the net force acting on the blocks. The force pushing and pulling the blocks can be split into two components:
1. The horizontal component of force: F_hor = 23.52 N
2. The vertical component of force: F_ver = 0 N (since the contact surfaces between the blocks are frictionless)
To find the net force, we need to consider the forces acting on the blocks in the horizontal direction:
1. The force pushing block A: F_A = 23.52 N
2. The force of friction acting on block A: f_friction_A = μ * F_N_A, where μ is the coefficient of friction and F_N_A is the normal force on block A.
Since the blocks are in contact with a horizontal surface, the normal force acting on block A is its weight, which is equal to its mass multiplied by the acceleration due to gravity (mg). Similarly, the normal force on block B is also the weight of B.
Next, we need to find the force of friction acting on block A. The force of friction can be calculated using the equation f_friction_A = μ * F_N_A. The coefficient of friction given is 0.29.
Finally, we subtract the force of friction on block A from the horizontal component of the applied force to find the net force:
Net force = F_hor - f_friction_A
Once we have the net force, we can use Newton's second law to find the acceleration:
Net force = mass * acceleration
Since the two blocks are connected, they will have the same acceleration (a).
Therefore, the magnitude of the acceleration of the blocks (a) can be found by rearranging the equation:
a = Net force / (mass of block A + mass of block B)
To summarize the steps:
1. Calculate the normal force on block A and B:
Normal force on block A = mg
Normal force on block B = mg
2. Calculate the force of friction on block A:
Force of friction on block A = μ * F_N_A
3. Calculate the net force:
Net force = F_hor - f_friction_A
4. Calculate the acceleration:
a = Net force / (mass of block A + mass of block B)
Plug in the given values and solve the equations to calculate the magnitude of the acceleration (a) of the blocks.