Why does the “Shoot the Monkey” demonstration work? Only weight present as a force. Newton says constant force implies constant acceleration. y x Starting Velocity V 0,y V 0,x H D

Gun fires and monkey drops at t=0 At some time T the dart has moved D in the x direction. Monkey and dart have the same horizontal position! What is the monkey’s vertical position at T? What is the dart’s vertical position at T? We need to compare H to v 0,y T. Our drawing will help! But! Do they have the same vertical position?

So H=v 0,y T. The dart and monkey are at the same place at the same time! Starting Velocity V 0,y V 0,x H D=v 0,x T Look at the green and dashed triangles. They are similar. If T times the base of the green triangle gives the base of the dashed triangle, what does T times the altitude of the green triangle give?

And Zip the monkey met his fate.

1.3 Ramps

Why are ramps so handy? Which is easier?

Observations About Ramps Lifting an object straight up is often difficult Pushing the object up a ramp is usually easier The ease depends on the ramp’s steepness Shallow ramps require only gentle pushes You seem to get something for nothing

Clicker question A ramp makes lifting a box easier because… A) You can use less energy to lift the box B) The ramp exerts some force on the box C) A ramp lets you stop for a drink

Forces Present Forces Present On the table (and the ball) due to the weight of the ball (mg) W=mg On the ball due to the support from the table (F support ) These forces have the same magnitude for a ball that’s not accelerating F support

Newton’s Third Law For every force that one object exerts on a second object, there is an equal but oppositely directed force that the second object exerts on the first object. To every action there is an equal and opposite reaction

This can be hard to believe sometimes! But you can’t escape it

Forces on a Ramp ( No Friction ) Weight or mg Support Force or F support Net Force along ramp

And you only have to overcome a smaller force when you use a ramp! Weight or mg Support Force Force along ramp from weight You have to apply a force that’s smaller than the weight to accelerate the box

What is wrong with this picture?

But you don’t get something for nothing! Introducing a new idea – WORK and ENERGY W=F d

Work is defined as the force parallel to the displacement times the displacement: W = F ll x d

Work = Force (along direction of motion) x distance Straight Lifting: 300 lb. x 6 ft. = 1800 ft-lbs Up Ramp: 90 lb. x 20 ft. = 1800 ft-lbs (same work, less force) W = F ll x d

Lift – Big Force times Small Distance Slide – Small Force times Big Distance Each product must be the same. Find WORK for lifting or sliding.

Energy and Work Kinetic energy: energy of motion KE = ½ mv 2 Potential Energy: Stored energy gravitational PE = mgh Energy: Capacity to do Work Work: Transferring energy W = F ll x d ENERGY IS ALWAYS CONSERVED

Recap: clicker question A. Bender exerts a bigger force on Homer B. Bender exerts a smaller force on Homer C. Bender exerts the same force on Homer When Homer exerts a force on hard, metallic Bender by punching Bender with his soft, fleshy hand…