We will approach this problem by looking at the pulley. There are 3 forces applied to the pulley, tension from each weight as well as its internal friction force. To clarify, we will denote that forces in the counterclockwise direction will be positive and forces in the clockwise direction are negative. Also, we need to remember that the internal static friction can be applied in both the clockwise and counterclockwise direction. This will create 2 scenarios. Let's first began when friction is applied in the counter clockwise direction. We will start with Newton's 2nd law:

Since we are asked to find when the system remains at rest, that means the net force on the system is 0:

Now we can begin looking at the three forces. First, we have tension created from mass A. This will be positive since it is in the counterclockwise direction relative to the pulley:

Next we have mass B which will be negative since it's in the opposite direction:

Lastly we have static friction which is positive in this scenario:

Now adding these together to get equation (1):

Rearranging for mass B:

Note that anything greater will result in the system moving.

Now moving onto the 2nd scenario. Let's just jump back to equation (1) and simply reverse the direction of static friction:

Note that anything less than this will result in the system moving. Therefore, the range of mass B that will keep the system stationary is:

We will use the sum of forces to solve this equation.

The Red Team will win this match of tug of war by pulling with  of extra force compared to the Blue Team. 

To solve this question use Newton's second law and the sum of forces to solve. First, before we solve we have to get our given values into the proper units.

Now we have to solve for the sport car's acceleration

Now use the net forces to solve.

Looking at the equation for weight. Notice, weight and acceleration are directly proportional. Thus what happens to the acceleration also happens to the weight. 

The acceleration due to gravity on the Moon is  that on Earth.

The ball will weigh  it's original value on Earth. 

Use Newton's second law to determine the car's acceleration. 

Now use a kinematic equation to solve for the time required.

The bag is on a flat surface, thus the normal force is equal to the weight of the bag.

Use the equation for kinetic friction to solve for the kinetic friction. 

Now use the sum of forces to solve for the net force acting on the bag.

There will be a total of  acting on the bag as it is pulled across the ground. 

Firstly, put the given values into the proper units. 

Now use Newton's second law to determine the acceleration.

He will decelerate at .

The bucket is not accelerating in either direction so the tension force must be equal to the weight of the groceries.

Multiplying mass and gravity gives weight

Plug in and solve for the mass

Kaden can carry a maximum of  of groceries in each load up to his balcony. 

First, convert to metric units.

Now, use the equation for velocity.

Plug in and solve for the final time.

Now use the equation for acceleration.

Plug in and solve for the acceleration.

Use Newton's second law to solve for the force.

Plug in and solve for the force that the catcher exerts on the ball.

The catcher will exert an amazing  of force to stop the fastball in such a short distance.

The weight is being compensated by the normal force.

Weight is equal to mass times the acceleration due to gravity.

The sled does not have to accelerate so the kinetic frictional force is equal to the pulling force .

The equation for kinetic frictional force is inserted below.

Plug in and solve for the pulling force.

Cody must apply at least  of horizontal pulling force.