Introduction to Forces - High School Physics

For this problem, we need to break the forces into horizontal and vertical components. The only difference with an inclined plane is that you have to translate the horizontal plane to be parallel to the surface upon which the object is traveling, and the vertical plane to be perpendicular to the surface upon which the object is traveling.

Luckily, this is already done in the diagram, with the force of gravity () broken into the vertical component () and horizontal component ().

Now, we need to sum the forces in each plane. The forces in the vertical plane will be perpendicular to the surface: and .

Since and are opposite and equal forces:

There is no net force in the vertical plane. This makes sense, as we would not expect the object to have any movement perpendicular to the surface on which it is sliding.

Now we can sum the horizontal forces: and .

Note that is positive and V is negative. This is because represents the force of friction, and is opposite to the force of .

Since there is no force in the vertical plane, this gives our final net force:

The normal force is always perpendicular to the surface upon which the object is moving, and is pointed away from said surface. That means we are looking for the value for in the diagram.

Observe that and are equal, but opposite forces.

If we can solve for , then we can find .

We can use our understanding of trigonometry to find an equation for .

If we plug in a for the angle, we see:

Since we are solving for Y, we can multiply both sides by W.

Now that we know an equation for , we can return to our original equation to solve for .

From here, we can use Newton's second law to find the value of , the total force of gravity.

Substitute this into our equation for .

Now we can solve for using the values given in the question for the angle, mass, and gravity.

Once the ball leaves your hand, there is no longer a contact force applied on the ball in the upward direction. There are no horizontal forces at work either. The only force acting on the ball is gravity. Gravity points in the downward direction. Therefore Diagram A is the correct answer.

Begin by identifying what forces are acting on the car. To start, the car has weight (the gravitational force) acting on it. This force points down. The car also has a normal force acting on it keeping it from falling through the road. This force points upward and is equal in magnitude (size) to the weight force. The car is accelerating, in the horizontal direction, which means that the forces must be unbalanced. If the forces were balanced in the horizontal direction, the car would either not be moving or moving at a constant velocity. The car likely is also undergoing friction which would be less than the accelerating force. Therefore diagram C is correct as there is an unbalanced force in the horizontal direction with a friction force opposing the motion.

Begin by identifying the forces on the book. The book has a weight (gravitational force) pushing down on it. The book is sitting on a desk, therefore the desk has an upward normal force acting on the book keeping it from falling through the desk which is equal in magnitude (size) to the gravitational force. The book is being pushed from the side meaning there are horizontal forces at work. The first is an applied force, the second is a force of friction against the motion. Since the book is moving at a constant velocity, the book is not accelerating. This means that the forces must be balanced. Therefore Diagram B is the correct answer as the horizontal forces are balanced.

Force is given by the product of mass and acceleration. If an object has a constant velocity, then it has no acceleration.

If an object has no acceleration, then it must also have no net force.

No additional information is needed to solve this question.

Once the ball leaves the bat, there is no longer a contact force applied on the ball in the upward direction. There are no horizontal forces at work either. The only force acting on the ball is gravity. Gravity points in the downward direction.

If the drop is at rest, then that means that the net forces acting upon it are equal to zero. There are two forces acting on the drop: the force due to gravity and the frictional force of the paint on the wall.

Mathematically, we can set up an equation for the net force:

The forces of friction and gravity are going to be equal and opposite, causing the drop to remain still on the wall.

For this problem, we are looking at the net force on the bone. Since both dogs are pulling with the same force, we can say the magnitude of the force of dog 1 equals the magnitude of the force of dog 2, but in opposite directions. Mathematically, .

To find the net force on the bone, we add the individual forces together.

We can substitute our forces into the equation for net force.

The net force is zero. Each dog pulls with equal force in opposite directions, allowing the total force to cancel out.

According to Newton's second law, . If the net force is zero, then the acceleration of the bone must also be zero.

If the drop is at rest, then that means that the net forces acting upon it are equal to zero. There are two forces acting on the drop: the force due to gravity and the frictional force of the paint on the wall.

Mathematically, we can set up an equation for the net force:

The forces of friction and gravity are going to be equal and opposite, causing the drop to remain still on the wall.

If two forces act on a single object, then the net force on the object is equal to the sum of the forces acting on it.

Forces are vector quantities, however. This means that all forces have a magnitude and a direction of action. When adding forces, we must take their directions into account. Directions are broken into horizontal and vertical portions for vector addition, and can be positive or negative based on the direction along the axis.

For a net force to be zero, one force must be positive and the other must be negative along a given axis. If the forces are of equal magnitude, then they must be acting in exactly opposite directions in order to cancel each other.

Kinetic force is not a technically correct property. Kinetic energy can be used to generate force, but is not a force in itself. Forces require non-zero acceleration, meaning that they only exist when there is a changein velocity. A change in kinetic energy can indicate a change in velocity, leading to a non-zero force value.

Normal force is the force of a surface upon an object, frequently countering gravity. Friction force is the resistance between an object and a surface, and acts opposite the direction of the object's motion. Buoyant force is the upward force of a fluid on a submerged object. Drag, or air resistance, is a special form of friction force for an object moving through a fluid.

First, realize that the force that the lighter child exerts on heavier child is equal and opposite to the force the heavier child exerts on the lighter child, as per Newton's third law.

Using Newton's second law, we can re-write this equation.

The question tells us that , making the heavier child and the lighter child. We can use this in our equation as well.

We are looking for the ratio of to , so we need to rearrange the equation.

First, the masses cancel out.

Then, divide both sides by .

The ratio of to is .

Newton's second law states that . We know the mass, but we need to calculate the acceleration.

Acceleration is the change in velocity per unit time.

Since the velocity does not change from one moment to the next, then there must be no net acceleration on the object.

Returning to Newton's second law, we can see that if there is no acceleration, then there is no net force.

The relationship between force and acceleration is .

Since the crate has a constant velocity, it has no acceleration.

If there is zero acceleration, that means there is no net force on the object, or .

The equation for a force is:

We can write this equation in terms of each object:

We know that the force applied to each object will be equal, so we can set these equations equal to each other.

We know that the second object is twice the mass of the first.

We can cancel out the mass from each side, leaving a relationship between the two accelerations.

The acceleration on the first mass is twice the acceleration on the second; thus, the acceleration of the lighter mass is greater.

Acceleration results from a change in velocity. Despite the speed remaining constant, velocity is a vector quantity and will change if the car changes direction. In rounding the turn, there is a change in the direction of the velocity, but not in the magnitude. This change in direction causes a non-zero acceleration.

The acceleration will remain equal to the equation for centripetal acceleration:

As long as the magnitude of the velocity and the radius of the turn do not change, the acceleration will remain constant.

If there are no forces acting upon the object, then there is no acceleration. If there is no acceleration, then the object will move with a constant velocity.

Mathematically, we can look at Newton's second law and the formula for acceleration.

We know that the force is zero.

Since we know that the mass cannot be zero, the acceleration must be zero.

We can now use the formula for acceleration to see the effects on velocity.

We know that the acceleration is zero and that the time is ten seconds.

In order for this to be true, the initial and final velocities must be equal.

The formula for force is Newton's second law:

We are told in the question to use for the mass and for the force.

Now we can isolate the acceleration.

This also makes sense from a units perspective. Units for force are Newtons, which can be written as:

In our equation, we can see that Newtons are divided by mass:

This would result in the units for acceleration.