Newton's second law allows us to solve for the force of gravity on the ball:

Newton's third law tells us that the force of the ball on the table, due to gravity, will be equal and opposite to the normal force of the table on the ball.

Substitute the equation for force of gravity.

Now we can use the mass of the ball and the acceleration of gravity to solve for the normal force. First, convert the mass to kilograms. Then, use the equation to find the normal force.

Newton's second law states that force is a mass times an acceleration.

In order for a force to exist, there must be an acceleration applied to a mass. A force cannot exist on a massless object, nor can it exist without a net acceleration.

Newton's third law states that for every force on an object, there is an equal and opposite force from the object. These force frequently cancel out, however, and produce a net force of zero.

Newtonian mechanics apply to all objects of substantial mass travelling at significantly slower than the speed of light.

Newton's law of universal gravitation, Newton's second law, momentum, and the equation for mechanical energy all fall under Newtonian mechanics.

The mass-energy equivalence suggests that mass can change as the speed of an object (such as an electron) approaches the speed of light. Newtonian mechanics assume that mass is constant, and do not apply to objects approaching the speed of light.

When you are slowing down the car, the fuzzy dice want to keep moving forward.  Therefore the angle they make will be toward the windshield.  The force of tension on the fuzzy dice is what is holding them back with the car, keeping them from going through the windshield.  This tension force is comprised of two components.  The y-component of the tension is equal to the force of gravity acting on the fuzzy dice.  The x-component of the tension is equal to the force of the car slowing down.

The angle of the fuzzy dice is related to these two components through the trigonometric function tangent.

We can then use in the inverse tan function to determine the angle acting on the fuzzy dice.

Notice how the mass of the dice falls out of the equation

We can now plug in our values and solve.

First we need to find the net force, which will be equal to the sum of the forces on the bone.

Since the forces are going in opposite directions, we know that one force will be negative (since force is a vector). Conventionally, right is assigned a positive directional value. The force to the left will be negative.

From here we can use Newton's second law to expand the force and solve for the acceleration, using the mass of the bone.

Newton's second law states that  .

If Derek is pushing with  of force, then we should be able to solve for the acceleration of the  crate.

Derek observes that the crate is acceleration at a rate of , rather than the expected . An outside force is acting upon it to slow the acceleration.

The equation for the net force on the object is: . We also know, from Newton's second law, that F resultant=ma resultant, where the resultant force and acceleration are the values actually observed.

Plug in the information we've been given so far to find the force of friction.

Subtract  from both sides to find the force of friction.

Friction will be negative because it acts in the direction opposite to the force of Derek.

Newton's second law states that force is a mass times an acceleration.

Since both masses have the same force acting on it, we can look at the relationship between mass and acceleration.  These two things are inversely proportional to one another.  As one increases, the other decreases.  Therefore the larger mass will have a smaller acceleration.  The smaller mass will have a larger acceleration.

Suppose that the force acting on both objects is .  We can confirm this by solving for the acceleration.

The smaller mass will accelerate 6 times faster than the smaller mass.

Newton's second law states that force is a mass times an acceleration.

Assuming that all the original values were equal to 

We can substitute in new values for a doubled force and quadrupled mass to find the new acceleration.

This shows that the new acceleration will be  of the original value or equal to a/2.

Newton's second law states that force is a mass times an acceleration.

In order for a force to exist, there must be an acceleration applied to a mass. A force cannot exist on a massless object, nor can it exist without a net acceleration.

Newton's third law states that for every force on an object, there is an equal and opposite force from the object. These forces frequently cancel out, however, and produce a net force of zero.

To solve this problem we need to divide up the situation into two parts.  During the first part the person is jumping from the roof of a house and is therefore undergoing freefall and accelerated motion due to the force of gravity.  Therefore we will need to use kinematic equations to solve for the final velocity as the person lands.  In the second part of the problem, the person decelerates their torso through a specific distance and comes to a stop.  We will then need to calculate the acceleration of the torso during this second part to determine the average force applied.

Let us start with kinematics to determine the speed of the torso as it hits the ground.

Knowns

We can use the kinematic equation

This is the velocity of the torso as it hits the ground.  We will know use the same equation with new variables to determine the acceleration of the torso as it comes to a stop.

Knowns

Rearrange to get the acceleration by itself

We can now plug this into Newton’s 2nd Law to find the average force acting on the object.