We begin by drawing a free body diagram of the block.

 is the force applied to the block.

 is the weight of the block, or the force due to gravity. Weight is defined as  where  is the mass of the block and  is the gravitational constant.

 is the normal force acting perpendicular to the contact surface.

 is the force due to kinetic friction. Friction is defined as  where  is the coefficient of friction.

 To find the force due to friction, we need to find  by applying Newton's second in the y-direction. 

Newton's second law is  where  is the net force,  is the mass of the block and  is the acceleration.

 There are two forces in the y-direction,  and . There are in opposite directions, so they are subtracted. We are given . There is no acceleration in the y-direction, so .

Substituting all this information into Newton's second law gives us

Assuming , 

Now that we have , we can find the force due to friction. Given that  and 

We now apply Newton's second law in the direction of acceleration.  In this problem, that is the x-direction. 

There are two forces in the direction of acceleration,the applied force  and the force due to friction . Assuming that  is applied in the direction of acceleration and  is in the opposite direction,

. The problem tells us  and . Substituting this information into Newton's second law gives us

We begin by drawing a free body diagram of the block.

 is the force applied to the block.

 is the weight of the block, or the force due to gravity. Weight is defined as  where  is the mass of the block and  is the gravitational constant.

 is the normal force acting perpendicular to the contact surface.

 is the force due to kinetic friction. Friction is defined as  where  is the coefficient of friction.

 To find the force due to friction, we need to find  by applying Newton's second in the y-direction. 

Newton's second law is  where  is the net force,  is the mass of the block and  is the acceleration.

There are two forces in the y-direction,  and . There are in opposite directions, so they are subtracted. We are given . There is no acceleration in the y-direction, so .

Substituting all this information into Newton's second law gives us

Assuming , 

Now that we have , we can find the force due to friction.  Given that  and ,

We now apply Newton's second law in the direction of acceleration. In this problem, that is the x-direction.

There are two forces in the direction of acceleration, the applied force  and the force due to friction . Assuming that  is applied in the direction of acceleration and  is in the opposite direction,

.  The problem tells us  and . Substituting this information into Newton's second law gives us

To solve this question, we need to determine how the acceleration of the system changes once the top box is removed. To do this, we'll first have to evaluate the acceleration of the system before the top box is removed, and then do the same after its removal.

First, let's determine the initial acceleration. Since the applied force is causing both boxes to accelerate, we know that the total mass of the system has to be the combination of the masses of both boxes.

Next, we can write an expression for the final acceleration of the system, which will only consist of the bottom box.

Since the force applied doesn't change in either instance, we can relate each of the two expressions shown above.

Next, we can rearrange the above expression to isolate the term for final acceleration.

Now, we just need to plug in the values that we know to obtain our answer.

Acceleration can be found by dividing the sum of the forces acting on an object by the mass of the object:

It is important to notice that both acceleration and the forces in the equation are vectors, meaning that both magnitude and direction matter.

In physics, we usually assign up and right as the positive directions, and down and left as the negative directions.

With that in mind, we first sum the forces:

Because our result is positive, the sum of the forces is directed towards the right.

Plugging in our sum and given mass in to our acceleration equation we find:

The person's perceived weight is a result of gravity and the elevator's acceleration changing the normal force between person and elevator. Using Newton's second law, we can express all of the forces in the y-direction as:

. Plugging in known values gives that 

The only forces acting on the helicopter are the upward mechanical force and gravity. Newton's second law gives that the net force can be given by . The total acceleration can then be expressed as .

Using kinematics, we can find the time the helicopter is airborne. Using this kinematic equation , we can plug in known values and solve for time:

 and 

The only forces acting on the person are gravity and an unidentified opposing force that slows the person's descent.

Using kinematics, we can find the net acceleration of the person:

. Plugging in our known values, we find  and .

Using Newton's second law, we know that

. All of the forces in the y-direction can then be expressed as . Solving for  we find that 

This question is testing your understanding of Newton's third law (equal and opposite forces). The forces between the cat and table depend solely on the mass of the cat; therefore, the mass of the table is irrelevant.

The force that the cat applies to the table is simply its weight. According to Newton's third law, the table also applies a force to the cat of the same magnitude. The force on the cat from the table is:

Since the two blocks are connected by the rope of the pulley, they will have the same acceleration and we can treat them as a single system. Start by drawing a free-body diagram including all the forces acting on each object.  Also, choose a direction to be considered the positive direction (+) and a direction to be the negative direction (-).

Each block has two forces acting on it: weight and tension. The weight of each block can be found using the equation:

Therefore, the weight of the 10 kg block is 100 N, and the weight of the 15 kg block is 150 N.

According to Newton's third law, for every force there is an equal and opposite force. The two tension forces, in this case, are an action/reaction pair; they are equal in magnitude but opposite in direction.

Now, using Newton's second law:

Since we are treating the system as a whole, or as if it is moving as a single object, we will add up all the forces acting on each object.

All forces which point in the positive (+) direction, as shown in the free body diagram above, will also be positive when put into the equation. All forces pointing in the negative (-) direction will also be negative in the equation.

What should we use for "" in the equation? Since we are treating the whole system as a single object, we must add all the masses together. In other words, 10 kg plus 15 kg, which is 25 kg total mass.

Notice now that the two tension forces will be canceled out, since they are action/reaction pairs and thus are equal but opposite in sign. So, solve for acceleration:

Dave weighs 589 N. This means his mass is

He accelerates at , which means he was pushed by a force of

By Newton's third law of motion, Dave must also have pushed of the ground with a force of 240 Newtons.