Fundamentals of Force and Newton's Laws - AP Physics 1

The correct answer is "Newton's First Law: every object continues in its state of rest or of uniform velocity in a straight line as long as no net force acts on it." On a slippery surface, we can assume there is no friction. If there is no friction working against the box's movement, the box will continue to move at its initial velocity forever. If the box were on a rough surface, friction from the surface would act against the box, causing the box's velocity to slow and eventually stop (if the force acting on the box is not greater than that of the frictional force).

According to Newton's first law, an object will remain at rest until a force is applied. If the floor of the boxcar is perfectly motionless, than the object will remain in the same spot in relation to the earth. This will make it appear to move to the back of the boxcar.

Force is defined as

Since the velocity is constant, the acceleration is zero. Therefore the force required to keep this object in motion is zero.

This is also stated in Newton's First Law: "An object will remain at rest or in uniform motion in a straight line unless acted upon by an external force."

According to Newton's First Law of Motion, an object that is in motion will stay in motion unless acted on by another force. When the van slows down, the ball will want to continue moving forward, and the friction between it and the floor of the van is not strong enough to keep the ball back.

The car and the truck experience equal and opposite forces, but since the car has a smaller mass it will experience greater acceleration than the truck according to the equation F = ma.

A greater mass will decrease the acceleration.

Use Newton's second law to solve this problem.

When the elevator is not moving, we get

However, when the elevator is accelerating downward, the man appears to be lighter since the elevator is negating some of the force from gravity. Written as an equation, we have:

Where is acceleration due to gravity and is the acceleration of the elevator.

Putting in our values, we get:

This question is testing your understanding of terminal velocity and Newton's second law. Since the skydiver is at terminal velocity, the force of the air is equal to the force of gravity, resulting in zero net force and thus no acceleration. We just need to calculate the force of gravity on the skydiver to find the force of the air:

There are two forces in play in this scenario. The first is gravity, and the second is air resistance. Since they are opposing each other, we can write:

Substituting in Newton's second law, we get:

Rearranging for the force of air resistance, we get:

Plugging in our values from the problem statement:

The free body diagram of the block is given above. This block has three forces acting on it. First, it's weight under the influence of gravity, which is given as . Second, the normal force of the plane, which is given as . Third, the friction force, which acts opposite to its direction of motion and is given as . We choose a coordinate system so that our x-axis aligns with the motion of the block down the plane, and the y-axis aligns with the direction of the normal force. Thus the friction force points in the negative direction of the x-axis, and the normal force is aligned with the positive direction of the y-axis. However, the weight is not along either of these axes, so we resolve the force into its components, along the negative y-axis, and along the positive x-axis.

Now we can use Newton's 2nd law to relate the given forces above. Newton's 2nd law gives us two equations:

and

Because the block is constrained to move along the surface of the inclined plane, there should be no acceleration in the y direction, and so . Also, because the block moves at constant velocity down the plane, Newton's 1st law assures us that there is no acceleration in the x direction as well, therefore . Plugging these accelerations in, we find that and

Summing all the forces in the x-direction gives us

Summing all the forces in the y-direction gives us

Plugging these values into the force equations above gives us the following equations:

Solving for in the second equation gives us . Thus the normal force is equal to the cosine component of the weight. Substituting in for in the first equation will give us the following:

Now we solve the equation for . Adding to each side gives us:

Now we divide each side by to obtain:

The final result is obtained by canceling the factor and using the triginometric identity:

Therefore we arrive at the conclusion that

Newton's first law of motion refers to objects with no external forces acting on them. Objects with no external forces will maintain the same velocity, meaning that

(1) if they are not moving, they will continue not moving

(2) if they are moving, they will keep moving with the same speed and direction

The answer "Dropping a box causes it to accelerate downwards" refers to a box with a force acting upon it—the force of gravity. Also, the box is accelerating, unlike objects referred to by Newton's first law of motion, which have constant velocities.

Since both you and your friend are traveling at a constant speed, the acceleration of you and your friend is zero. Thus, neither you nor your friend experiences any acceleration. This can be shown mathematically using the equation for acceleration:

Since there is no change in velocity over time acceleration is zero. Also note that when acceleration is zero, so is the net force.

Because an object at rest tends to stay at rest, when your car is hit your body/neck will 'want' to stay where it was. This will cause your body and neck to 'whip' as it will take time for it to speed up from being hit.

According to Newton's First Law of Motion, something in motion will stay in motion unless acted on by another force. As the van slows down, we expect free object in the van to continue moving forward within the van. However, helium is lighter than air so the air in the van will continue to move forward, leaving the light balloons in the back of the van.

Finding initial momentum:

Combining equations:

Plugging in values:

Combining equations:

Converting to and plugging in values:

Using

Plugging in values:

Using:

Solving for and plugging in values

Before we start using equations, we need to determine what forces are acting on the block in this system. The only relevant forces in this situation are gravity and friction. We are given the acceleration of the block, giving us the tools to find the net force.

Using Newton's second law, we can write:

The force of friction is subtracted because it is in the opposite direction of the movement of the block. Substituting in expressions for each variable, we get:

Canceling out mass and rearranging for the coefficient of kinetic friction, we get:

We have values for each variable, allowing us to solve:

There are two relevant forces acting on the block in this scenario: gravity and friction. We can use Newton's second law to solve this problem:

Substituting in expressions for each force, we get:

Eliminating mass and rearranging for , we get:

At this point, we can plug in values for each variable and solve:

Start by drawing in the forces acting on each block. You could also draw in the force of gravity and the normal force for each block, but they have been omitted from the image because they cancel each other out for each block and because there is no friction in this problem.

We are given in the question that the force is 100 N. Since the blocks are connected by a string, they will therefore accelerate at the same rate, and we can treat them as a system that moves as if it were one object of total mass 80 kg (30 kg plus 50 kg). Use Newton's second law:

In this problem, the two tension forces form an action/reaction pair and therefore are equal in magnitude but opposite in direction (Newton's third law). So:

We can solve for acceleration, since the tensions cancel out.

Now that we have acceleration, we need to write a new equation in which the tension force does not cancel out so that we can solve for the tension .

Do this by using Newton's second law again, except for only one of the blocks:

Lets consider the 30 kg block. The only force acting on the 30 kg block is the tension , and the acceleration is what we found above.

The normal force is perpendicular to the plane:

First, we need to find .

We can solve for using the trigonometric equation that applies in this instance. We know the length of the side opposite of (5 m) and the length of the side adjacent to (10 m), so we can use the following equation to solve for :

Rearranging to solve this equation for , you get

Substituting in the side lengths of the given triangle, we can solve for .

Note that the normal force is one of the legs of another right triangle. The other leg is the parallel force, and the hypotenuse is the force of gravity.

Using trigonometry, we know that

because , or, in terms of this problem, .

Substituting in the known values into this equation, we can solve for the normal force:

Consistent with Newton's third law, which states that every force has an equal and opposite reaction, the force on the rifle is equal to the force on the bulet. However, the rifle has a larger mass, so the magnitude of its acceleration is less than that of the bullet.

The component of perpendicular to the slope is , where is the angle between the ground and the incline.

where is the normal force.

The force of friction, which is in the direction opposing motion is:

is the coefficient of kinetic friction.

The component of parallel to the slope is:

The net force on the block is: