Finding the Change in Velocity ^v = g x t The velocity of falling objects To find the change in velocity, multiply the acceleration due to gravity (g) by the time it takes for the object to fall in seconds (t):

For example: A stone is dropped from a cliff, and it takes 3 seconds to hit the ground. Its downward velocity when it hits the ground is as follows: ^v = 9.8 m/s / s x 3 s ( the seconds cancel each other =29.4 m/s

Now it’s your turn A penny at rest is dropped from the top of a tall stairwell. What is the penny’s velocity after it has fallen for 2 seconds? The penny hits the ground in 4.5 seconds. What is its final velocity?

You should have gotten… 1. 9.8 m/s / s x 2 s = 19.6 m/s 9.8 m/s / s x 4.5 s = 44.1 m/s

Try it again… 1. A boy standing on a high cliff dives into the ocean below and strikes the water after 3 seconds. What is the boy’s velocity when he hits the water? 2. A rock falls from a high cliff and hits the ground in 6.5 seconds. What is its final velocity? 3. A brick falls from the top of a building and strikes the ground with a velocity of 19.6 m/s How long does the brick fall?

Did you get… 1. 29.4 m/s 2. 63.7 m/s 3. 2 seconds

Is That a Fact!!! Air resistence is a result of the fluid friction between the falling object and the air and also the inertia of the particles have to “ move out of the way” of the falling object. Because the particles have mass, they also have inertia that resists movement.

Weird Science If a penny fell from the top of the empire state Building ( about 385 m), it would be traveling with enough velocity to dent almost anything it struck at ground level.

Newton’s second law of motion and mathematical problems How to find acceleration: a= F/ m the relationship of acceleration (a) to mass (m) and force (F) can be expressed mathematically with the above equation. It can be rearranged to the following form: F= m x a

Both forms of the equation can be used to solve problems. Newton’s second law explains why objects fall to Earth with the same acceleration.

For example: The apple and the watermelon An apple has less mass, so the gravitional force on it is smaller. However, the apple also has less inertia and is easier to move. The watermelon has more mass and therefore more inertia, so it s harder to move.

See the problem for the apple.. M=0.102 kg F = 1 N 1 N = 1 kg. m/s/s a = 1 kg . m/s/s / 0.102 kg = 9.8 m/s/s

See the problem for the watermelon….. M = 1.02 kg F= 10 N 10 N = 10 kg. m/s/s a= 10 kg. m/s/s / 1.02 kg = 9.8 m/s/s The answers are the same proving that they fall at the same rate!

Try these… 1. What is the acceleration of 7 kg mass if a force of 68.6 N is used to move it toward the Earth? ( Hint: 1 N is equal to 1 kg . m/s/s) What force is necessary to accerelate a 1,250 kg car at a rate of 40 m/s/s? What is the mass of an object if a force of 34 N produces an acceleration of 4 m/s/s?

Did you get…. 1. a= F/ m= 68.6 N / 7 kg = 9.8 m/s/s (This is acceleration due to gravity.) 2. F = m x a = 1,250 kg x 40 m/s/s = 50,000 N 3. m = F/ a = 34 N / 4 m/s/s = 8.5 kg

Now try these Calculate the force of gravity acting on your 6 kg backpack. (this is the weight of your backpack.) A 50 kg skater pushes off from the wall with a force of 200 N. What is the skater’s acceleration?

Answers…. 1. F= 6 kg x 9.8 m/s/s = 58.8 N 2. 4 m/s/s

Work and Power Work occurs when force causes an object to move in the direction of the force. W = F x d The answer would be called a Joule (J) Force is expressed in Newtons (N)

Working It Out Use the equation for work shown to solve the following problem: A man applies a force of 500 N to push a truck 100 m ( meters) down the street. How much work does he do? W= F x d W =500 N x 100 m W = 50,000 N*m W= 50,000 J

Now you try…. 2. A man lifts a barbell using 80 Newtons of force a total distance of 1 meter. How much work is being done by the man?

The answer…. W= 80 N x 1 m W= 80 J

3. You have 160 N and 1 m, what is the amount of work? 4. You have 80 N and 2 m, what is the amount of work being done? 5. In which situation do you do more work? You lift a 75 N bowling ball 2 m off the floor. You lift two 50 N bowling balls 1 m off the floor.

The answers….. 3. 160 J 4. 160 J 5. Lifting the 75 N ball a distance of 2 m ( 150 J)

Power Power is the rate at which work is done. To calculate power (P), you divide the amount of work done (W) by the time (t) it takes to do that work P = W/t can also be P = J/t …same thing The first one is the one we will use. The unit to express power is Joules per second (J/s), which is more simply called watt (W).

If you do 50 J of work in 5 seconds, your power is 10 J/s, or 10 W. Try this: You do 100 J of work in 10 seconds, what is your power? 10 J/s

Mechanical Advantage Mechanical advantage= output force/input force MA= 500 N / 50 N = 10 N 1. You apply 200 N to a machine, and the machine applies 2,000 N to an object. What is the mechanical advantage? (10 N)

Mechanical Efficiency ME = work output/work input x 100 The 100 in this equation means that you are expressing this in percentage. For example: 500N ( output) / 50 N ( input) (= 10) x 100 ME= 1,000 %