Finding the Change in Velocity

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 %

Finding the Change in Velocity