Week 5 (Feb 10 - 14)
Read: and Naturally accelerated motion (ASGv2 Chap. 8). The Mean Speed Theorem (ASGv2 Ch. 9)
Key topics: uniform acceleration; position, velocity and acceleration, mean speed theorem
PHY 201 lecture: The calculus of kinematics and falling bodies: time derivatives, displacement, velocity and acceleration.
Key topics: uniform acceleration; position, velocity and acceleration, mean speed theorem
PHY 201 lecture: The calculus of kinematics and falling bodies: time derivatives, displacement, velocity and acceleration.
Homework:
Lab: Ramp laboratory (Ex. 10.2). To prepare for lab this week, I would strongly recommend that you watch the videos associated with Chapter 9 of A Student's Guide Volume 2. These videos explain the kinematic relationships between acceleration, velocity and position of a falling object. Then, in lab this week, we will place a cart on a ramp with a certain inclination. We will measure the force required to keep the cart from rolling down the ramp, and how this depends on the inclination of the ramp. We will then allow the cart to roll down the ramp at these various inclinations and we will measure the acceleration of the cart. How is the force required to suspend the cart, F, related to the acceleration it experiences, a, if the suspending force is removed? Be sure to make a (clearly labelled) plot of F vs a for various angles, theta.
Chapter 8: The following 6 videos discuss Galileo's ideas on falling bodies, uniform motion, and uniformly accelerated motion.
Chapter 9: The next 4 videos introduce the mean speed theorem. This is extremely useful for determining the distance travelled by a falling body.
- truth and error (Ex. 8.1),
- motion sketching (Ex. 8.2),
- Falling cannonball (Ex. 9.1),
- Ball toss (Ex. 9.2),
- An object is thrown straight up wards from the ground level with a speed of 50 m/s. What is its distance from the ground 6 seconds later? Answer: in five seconds, it will be at the peak of its flight; in 6 seconds it will have fallen back down for one second. The max height will be 125 meters. So at six seconds it will be at 120 meters.
- A ball is dropped from a 100 meter cliff. Assume that the acceleration due to gravity is 10 m/s^2. (a) What is the time it takes to strike the ground? (b) What is its speed when it strikes the ground? (c) Make a graph of the ball's (i) velocity versus time, (ii) acceleration versus time and (iii) height versus time. (d) If the ball is perfectly elastic, so that its motion is reversed when it hits the ground, then how long will it take to get back up to 100 meters? What will be its speed at the top of its flight? What will be its acceleration at the top of its flight?
- PHY 201: Castaway Kinematics (Ex. 9.3),
Lab: Ramp laboratory (Ex. 10.2). To prepare for lab this week, I would strongly recommend that you watch the videos associated with Chapter 9 of A Student's Guide Volume 2. These videos explain the kinematic relationships between acceleration, velocity and position of a falling object. Then, in lab this week, we will place a cart on a ramp with a certain inclination. We will measure the force required to keep the cart from rolling down the ramp, and how this depends on the inclination of the ramp. We will then allow the cart to roll down the ramp at these various inclinations and we will measure the acceleration of the cart. How is the force required to suspend the cart, F, related to the acceleration it experiences, a, if the suspending force is removed? Be sure to make a (clearly labelled) plot of F vs a for various angles, theta.
Chapter 8: The following 6 videos discuss Galileo's ideas on falling bodies, uniform motion, and uniformly accelerated motion.
Chapter 9: The next 4 videos introduce the mean speed theorem. This is extremely useful for determining the distance travelled by a falling body.