A 33.3- kg block (m1) is on a horizontal surface, connected to a 5.1- $kg$ block (m2) by a massless string. The pulley is massless and frictionless. A force of 220.1 N acts on m1 at an angle of 32.p deg. The coefficient of kinetic friction between m1 and the surface is 0.201. Determine the upward acceleration of m2.

To determine the upward acceleration of m2, we need to calculate the net force acting on m2 and use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.

First, let's calculate the net force acting on m2. The mass of m2 is given as 5.1 kg, and we can assume that the force acquired from m1 is acting in the upward direction.

The force acting on m2 can be calculated using the equation:

Force = mass * acceleration

The acceleration is what we need to find, so we will rearrange the equation:

Acceleration = Force / mass

We already have the mass of m2, so we need to determine the force. The force acquired from m1 can be calculated using the equation:

Force_m1 = Force_applied * cos(angle)

Substituting the given values into the equation:

Force_m1 = 220.1 N * cos(32°)

Next, we need to consider the friction force resistant to the motion of m1. The friction force can be determined using the equation:

Friction force = coefficient of friction * normal force

The normal force is the force perpendicular to the surface, which is equal to the weight of m1 in this case. So:

Friction force = coefficient of friction * weight_m1

The weight of m1 can be calculated using the equation:

Weight_m1 = mass_m1 * gravity

Substituting the given values:

Weight_m1 = 33.3 kg * 9.8 m/s^2

Now we can calculate the friction force:

Friction force = 0.201 * Weight_m1

Finally, we can determine the net force acting on m2:

Net force = Force_m1 - Friction force

Now, we can substitute this value for force and the mass of m2 into the equation for acceleration:

Acceleration = Net force / mass_m2

After performing these calculations, you will find the upward acceleration of m2.