Force and Work Unit Practice Quiz

Force is defined as a push or pull that can cause an object to undergo a change in motion. It is a vector quantity, having both magnitude and direction.

When equal and opposite forces act on an object, they cancel each other out, resulting in a net force of zero. This condition often indicates equilibrium.

Newton's First Law, the law of inertia, tells us that an object will remain at rest or in uniform motion unless an unbalanced force acts upon it. This principle is fundamental in understanding inertia.

Force is measured in newtons in the International System of Units (SI). The newton quantifies the amount of force required to accelerate a mass at a rate of 1 m/s².

Weight is a measure of the gravitational force on an object. It differs from mass, which is a measure of the amount of matter in the object.

Newton's Second Law is given by F = ma, so acceleration is a = F/m. With a force of 10 N and a mass of 2 kg, the acceleration is 5 m/s².

Net force is the vector sum of all forces acting on an object. Here, subtracting the frictional force from the applied force gives 20 N - 5 N = 15 N.

Work is calculated using the formula W = F × d when the force is applied in the same direction as the displacement. Therefore, 50 N × 4 m = 200 Joules.

The work-energy principle states that the work done on an object is converted into kinetic energy. An accelerating car clearly illustrates this conversion from chemical energy to kinetic energy.

The resultant force when forces are applied at an angle depends on both the magnitudes of the forces and the cosine of the angle between them. The angle determines how much of each force contributes to the net force.

Cosθ in the work formula accounts for the angle between the force and displacement vectors. It ensures that only the component of the force acting in the direction of displacement contributes to the work done.

Friction is the resistive force that opposes the motion or tendency of motion between two surfaces in contact. Its magnitude depends on the nature of the surfaces and the normal force between them.

When an object moves at a constant velocity, it indicates that the forces acting on it are balanced, resulting in a net force of zero. Consequently, there is no net work being done as there is no change in kinetic energy.

Static friction must be overcome to initiate motion, whereas kinetic friction acts on objects that are already moving. Typically, static friction is greater than kinetic friction.

First, calculate the acceleration as change in velocity divided by time: 20 m/s ÷ 10 s = 2 m/s². Using Newton's second law, F = m × a, we find F = 5 kg × 2 m/s² = 10 N.

To find the horizontal component, multiply the force by the cosine of the angle. Since cos(60°) equals 0.5, the horizontal component is 30 N × 0.5 = 15 N.

When two perpendicular forces act on an object, the resultant force can be determined using the Pythagorean theorem. Calculating √(40² + 30²) gives √(1600 + 900) = √2500 = 50 N.

First, calculate the frictional force using f = μmg = 0.3 × 10 kg × 9.8 m/s² ≈ 29.4 N. Subtract this from the applied force: 50 N - 29.4 N ≈ 20.6 N, then use Newton's second law: acceleration ≈ 20.6 N / 10 kg ≈ 2.1 m/s².

The cosine function separates the component of the force that is parallel to the displacement from the total force. This ensures that only the effective force doing work is considered in the calculation.

An inclined plane allows the workload to be spread out over a longer distance, reducing the force needed at any one moment. This is the principle of mechanical advantage, which makes lifting heavy loads easier.