Newton’s laws of motion

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Presentation transcript:

Newton’s laws of motion State Newton’s 1st and second laws Use N II to calculate magnitude and direction of a force

1687 – Principia Mathematica

1st law Every body continues in its current state of motion unless an external force acts upon it. So... An object at rest stays at rest An object that is moving continues with the same velocity Unless a force acts on it.

2nd law The force that acts on a body is directly proportional to its rate of change of momentum.

“The force that acts on a body is directly proportional to its rate of change of momentum.” Because we use the SI system, the constant is not needed Force equals rate of change of momentum.

Momentum Defined as Momentum = mass x velocity Kgm/s kg m/s

The symbol ‘p’ is often used. Thus, p = mv

A vector quantity Since velocity is a vector, so is momentum. By usual convention we take left to right as positive. As long as you consider carefully the direction it doesn’t really matter.

Example A car of mass 1600 kg accelerates from 0 to 25 m/s in a time of 6 s. Calculate: The acceleration The final momentum The net force acting on the car

Force and momentum Since force is equal to rate of change of momentum F = Δ mv Δt FΔt = mv - mu

Impulse FΔt or mv – mu is often called the ‘impulse.’ Show that the Newton-second is equivalent to the units of momentum.

Example A golf ball of mass 0.150 kg is initially at rest and gains a speed of 50m/s. Calculate the change in momentum. If the golf club is in contact for a time of 20ms, calculate the average force on the ball. Hence find the acceleration of the ball.

Example A cricket ball of mass 250 g is bowled at 15 m/s and returned by the batsman at 30 m/s in the opposite direction. The ball is in contact with the bat for 1/20th of a second. Calculate the force. Calculate the change in kinetic energy. The distance over which this force acted.

Force and Momentum A ball of mass 0.3 kg is kicked by a foot. The ball is initially at rest and acquires a velocity of 25 m/s. The foot is in contact with the ball for a time of 0.02 s. a) Calculate the momentum gained by the ball. b) Calculate the force acting on the ball.

A tennis ball is initially moving with velocity of 10 m/s when it hits a tennis racket. The ball is returned in the opposite direction with speed of 20 m/s. The ball has mass 0.15 kg. a) Calculate the momentum change of the ball. b) If the racket is in contact with the ball for 0.01 s, calculate the force acting on the ball.