AP Physics C: Unit 3 Practice MC (Shortened)

The speed of the pendulum ball at the low point is given by the formula: $$v = \frac{L}{g} \times \text{sin}(\theta)$$ , where L is the length of the pendulum, g is the acceleration due to gravity, and θ is the angle of release.

Average power is defined as the work done per unit time. It can be calculated using the formula: $$P = \frac{W}{t}$$ , where P is power, W is work, and t is time.

The work done by the force F is given by the formula: $$W = Fd \text{cos}(\theta)$$ , where d is the distance moved.

The kinetic energy of the marble is proportional to the square of the distance compressed. If the spring is compressed to distance x, the kinetic energy is $$KE_1$$ . If compressed to 4x, the kinetic energy becomes $$KE = 16KE_1$$ .

The principle states that the total mechanical energy (potential + kinetic) of the object remains constant if only conservative forces are acting. Energy lost to friction is the difference between initial and final mechanical energy.

Kinetic energy (KE) is the energy of an object due to its motion. The formula is: $$KE = \frac{1}{2}mv^2$$ , where m is mass and v is velocity.

The coefficient of friction (μ) quantifies the amount of frictional force resisting the motion of two surfaces in contact. It is used to calculate the frictional force as: $$F_f = \text{μ}mg$$ .

Energy lost to friction can be calculated by finding the difference between the initial potential energy and the final kinetic energy: $$E_{lost} = PE_{initial} - KE_{final}$$ .

The potential energy (PE) of an object at height h is given by: $$PE = mgh$$ , where m is mass, g is the acceleration due to gravity, and h is the height.

Constant velocity means that the object's speed and direction remain unchanged. This occurs when the net force acting on the object is zero, meaning all forces are balanced.