Engagement Suggestion:

Background:

The ball on the straight track retains essentially the same velocity and the same kinetic energy throughout the length of its run, the kinetic energy from the spring. The ball on the dipped track, however, has a more complex path. When it goes downhill, it gains kinetic energy from gravitational potential, accelerating it. It travels along the lower section of track with this increased kinetic energy, and thus greater velocity. The ball then goes uphill again, losing that additional kinetic energy – it has returned to the same height, so the principle of conservation of energy dictates that it must return to the same gravitational potential as before, giving up kinetic energy equal to what it gained. It now has only the same kinetic energy it started with, as imparted by the spring. So its velocity is now the same as its starting velocity, and the same as the velocity of the other ball.

However, during the time it was on the lowered section track, it had greater kinetic energy and greater velocity, so it traveled that distance faster than the ball on the straight track. And thus the ball on the dipped track reaches the end first, but with the same final velocity and the same final kinetic energy.

Engagement Suggestion

Background

The gravitational force on each of the cubes is the same, so they experience the same downward acceleration. So since they started from the same height with zero vertical velocity, they reach the floor at the same time, even though one has traveled some distance horizontally in the meantime.

This is an example of the independence or separability of the components of motion. We can define the axes along which we measure, and treat vectors as the sum of their components along those axes.

The launcher is aimed at the monkey and shot. As the projectile leaves the muzzle of the gun it breaks a circuit producing the magnetic field which holds the monkey in place. The monkey then begins to fall at the same time the projectile is fired directly at the monkey. Due to independence of horizontal and vertical components of motion, the projectile will strike the monkey.

Note that the angle can be varied to show different horizontal and vertical components.

Place the lead brick gently on your fingers and strike the lead brick sharply with the hammer. The inertia of the lead brick prevents damage to your fingers.

Engagement Suggestion

Engagement Suggestion:

Background:

Newton’s First Law of Motion states that an object’s velocity is constant unless there is a net force acting on it. What this means is that if an object is not moving (at rest), it will not start moving until there is a force pushing or pulling on it. If an object is moving at a constant speed and direction, it will keep going with that same speed and direction unless a force pushes or pulls on it to change that. When the pen is sitting on top of the hoop, the force of gravity is pulling it down, but the normal force of the hoop is exactly equal to the gravitational force and holds it up. If another force suddenly affects the pen (such as if you walk up and tap on its side, or jiggle the hoop up and down), that force could cause it to move, and probably fall.

But if the hoop is snatched sideways quickly and smoothly, it does not give any force to the pen. Now the only force acting on the pen is gravity, and the pen falls straight down into the bottle.

CAUTION: Be sure that the hose fitting is securely attached to the tube and that the plastic shield is in place before firing. The shield should be latched in place, with no debris blocking its edge from meeting the baseplate

Engagement Suggestions

• • Before using, encourage your students to predict what will happen to the pencil.
• • For advanced students, discuss the energy involved in the problem and where the kinetic energy of the pencil went after the collision.

Background

This demonstration can be presented in multiple ways. It has been offered classically as an illustration of the principle of inertia – the pencil is in motion at a high velocity, and continues in motion despite the intervening wood until arrested by a greater force. Alternatively, consider the high velocity and high momentum of the pencil. The abrupt deceleration at the plywood means a high impulse. The pointed pencil has a very small cross-sectional area, resulting in force applied over a small area leading to a high momentary pressure.

Linked below is a slow-motion video of the collision, shot at 600 frames per second. A fun class activity could be to use the video to measure the motion of the pencil and estimate its momentum and kinetic energy, based on what you see in the video and by measuring typical lengths and masses for wooden pencils.

Equal masses M of 200 grams are hung on the ends of a light string passing over a light, frictionless pulley. When an additional mass of 100g is hung on one end, the resulting acceleration can be measured by timing the motion of either mass over a distance S between two points. The acceleration of gravity g can then be calculated: g = a (2M + m)/m, where a is the acceleration of the system: a = 2S /t^2.

Background