Energy & Momentum: Note 1

Work

Work is the amount of energy transferred by a force over a certain distance. We can calculate work using: ! ! W = F ⋅ d where: -W is the amount of work in J (Nm) -F is force applied in N -d is displacement in m € *Note: This operation is a “vector dot product” which involves the multiplication of two vectors to produce a scalar quantity. This multiplication only works when the components of the vectors are pointing in the same direction. We can use the other form of the formula to find work (for when F is not parallel to d) where: -W is the amount of work in J (Nm) W = F d cos θ -F is force applied in N -d is displacement in m -θ is the angle the force is on compared to d € Conditions when NO WORK IS DONE: • When F is perpendicular to d (Eg. Carrying something) • When F = 0 (Eg. Skating at constant velocity) • When d = 0 (remember this is displacement, not distance) Work-Energy Theorem states that the amount of work done to a system will equal the change of energy of that system. The work that I do to throw a football will equal its kinetic energy when it flies through the air. Negative work occurs when the force applied is opposite to the direction of travel. Eg. If Superman is trying to stop a train from going over a cliff, he will go in front of it and try to push it backwards, thus slowing it down. The force he is applying is opposite to the direction of travel. Eg. 1. Ricky pushes a shopping cart in a circle of radius 5.00 m with a force of 12.0 N. a) How much work has he done after half a lap? b) How much work has he done after a full lap? Eg. 2. Ricky now needs to cut his lawn. He pushes his lawnmower with a force of 15.0 N over a displacement of 8.00 m. If the handle is on an angle of 30.0o, how much work has he done?

Energy & Momentum: Note 1 Energy Energy cannot be created or destroyed, only gained or lost in a system. This means that the amount of initial energy will equal the amount of final energy (while taking into account the energy gained/lost). In a system: E = E’ If energy is gained/lost: E ± W = E’ Kinetic Energy Kinetic energy is the energy associated with motion. It is found using information about an object’s mass and velocity: Ek = 1 mv 2 2 Gravitational Potential Energy GPE is energy that is stored when you increase the separation between two objects (in this case, between an object and Earth). It is found using an object’s mass and height. Eg = mgh Thermal Energy Thermal energy is the energy associated with temperature. If an object’s temperature increases, so does its thermal energy. To calculate thermal energy, we need to know an object’s mass, specific heat capacity, and its change in temperature: Q = mcΔT Eg. 3. A soccer player kicks a 0.43 kg soccer ball down a smooth (frictionless) hill 18.0 m high with an initial speed of 7.4 m/s. Calculate the ball’s speed when it reaches the bottom of the hill.