A 3.39 kg block is placed on top of a 11.8 kg
block. A horizontal force of F = 61.3 N is
applied to the 11.8 kg block, and the 3.39 kg
block is tied to the wall. The coefficient of
kinetic friction between all moving surfaces
is 0.112. There is friction both between the
massesandbetweenthe11.8kgblockandthe
ground.
The accelerationof gravityis9.8m/s2.
To find the acceleration of the system, we can use Newton's second law of motion, which states that the net force acting on an object equals the product of its mass and acceleration (F = ma).
First, let's determine the net force acting on the system. We have a 61.3 N force applied to the 11.8 kg block, and we need to account for the friction between the surfaces.
The frictional force can be calculated using the equation F_friction = μ * N, where μ is the coefficient of kinetic friction and N is the normal force. The normal force is the force exerted by a surface perpendicular to the object. In this case, the normal force is equal to the weight of the object.
For the 11.8 kg block, the weight can be calculated using the equation F_weight = m * g, where m is the mass and g is the acceleration due to gravity. So, the weight of the 11.8 kg block is (11.8 kg) * (9.8 m/s^2) = 115.64 N.
The normal force between the surfaces in contact is equal in magnitude but opposite in direction to the weight of the 11.8 kg block. Therefore, the normal force is -115.64 N. We take the negative sign to indicate that it opposes the gravitational force.
Now we can calculate the frictional force. F_friction = μ * N = (0.112) * (-115.64 N) = -12.95 N. Again, the negative sign indicates that the frictional force acts in the opposite direction of the applied force.
Next, we can find the net force acting on the system. The total force applied to the system is the force applied to the 11.8 kg block minus the frictional force: F_net = 61.3 N - (-12.95 N) = 74.25 N.
Finally, we can find the acceleration of the system using the net force and the combined mass of the two blocks. F_net = m_total * a, where m_total is the sum of the masses. m_total = 11.8 kg + 3.39 kg = 15.19 kg.
Substituting the values into the equation, we get 74.25 N = 15.19 kg * a. Solving for a, we find a = 4.88 m/s^2.
Therefore, the acceleration of the system is 4.88 m/s^2.