Study Guide for PHY211 Exam 3

Projectile motion: a projectile will undergo some displacement in the y-direction, where the acceleration is a_y = -g ĵ (up and down) in the exact same time as it takes to move along the x- direction to the final x-coordinate.

If an object is launched with an initial speed of 20 m/s at an angle of 25°, please do not use 20 m/s in any of the kinematics equations. You must break this up into the x and y components!!!

Conservation of Momentum: this is really Newton’s 3^rd Law written in a different way. Problem #4 from the 2^nd exam clearly illustrates this point. I asked you to solve the problem using Newton’s Laws i.e. F_net=ma, but it’s much simpler to use conservation of momentum. Whenever there is a collision, you should automatically think, p_i = p_f.

Inelastic and elastic collisions: Momentum is conserved in ANY collision UNLESS there is some external force acting on the system. Make sure to choose your system accordingly! If objects stick, the collision is inelastic and mechanical energy is NOT conserved. Mechanical energy is conserved during elastic collisions. We derived formulae for the final velocities of two objects colliding when one is initially at rest. Please use them if needed.

Work-Energy Theorem: the net work done on an object causes a change in the object’s kinetic energy. If you lift a book at constant speed, you do work on the book. The earth does an exact same amount, but it’s negative (why?). Therefore the net work done on the book is zero! So the change in kinetic energy of the book is zero.

The total work done is simply the area under a Force- position graph.

If a force is perpendicular to the motion (i.e perpendicular to the displacement), then the work done is zero! Only the component of the force in the direction of the displacement contributes to the work done, and is calculated by the ‘dot product’. We’ll cover this on Tuesday.

Simply put, if I have two vectors , then the dot product , where A is the magnitude of A, B is the magnitude of B (found by using Pythagorean’s theorem), and α is the angle between them. Note that this result is a scalar.

Springs: if I stretch a spring, then the spring exerts a force on me and is equal to

F = -k(x-x_eq), where x_eq is the equilibrium position of the spring, and x is my final position. The force applied to me is exactly opposite to the direction that I’m extending or compressing the spring. That’s the meaning of the minus sign.

The potential energy stored in the spring at any given instant is equal to

U_s = (1/2)k(x-x_eq)². So the total energy of the system is E_mech = K + U_s + U_g.

Power: power is the rate of transfer of energy, or

Since dE_sys=W_ext (W_ext = ):

The unit for power is J/s = Watt and is abbreviated as W. So your 100 W lightbulb uses 100 Joules of electrical energy each second that it’s on.