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Apparent Weight apparent weight - weight force that we actually sense not the downward force of gravity, but the normal (upward) force exerted by the surface we stand on - opposes gravity and prevents us falling to the center of the Earth - what is measured by a weighing scale.

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ISNS 4371 - Phenomena of Nature

Apparent Weight

apparent weight - weight force that we actually sense not the downward force of gravity, but the normal (upward) force exerted by the surface we stand on

- opposes gravity and prevents us falling to the center of the Earth - what is measured by a weighing scale.

For a body supported in a stationary position, normal force exactly balances earth's gravitational force

- apparent weight has the same magnitude as actual weight.

If no contact with any surface to provide such an opposing force - no sensation of weight (no apparent weight).

- free-fall - experienced by sky-divers and astronauts in orbit who feel "weightless" even though their bodies are still subject to the force of gravity - also known as microgravity.

A degree of reduction of apparent weight occurs, for example, in elevators. In an elevator, a spring scale will register a decrease in a person's (apparent) weight as the elevator starts to accelerate downwards. This is because the opposing force of the elevator's floor decreases as it accelerates away underneath one's feet.


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ISNS 4371 - Phenomena of Nature

Apparent Weight Animation


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ISNS 4371 - Phenomena of Nature

Friction is a Force That Affects Motion

Ff

Fg

FN

W

  • The force due to friction, Ff, is equal to the normal force, FN.

  • The block will slide when the friction force is equal to the component of the gravitational force in the direction along the plane, Fg.

  • From simple trigonometry:

  • Ff = Wcos()

  • Where  is the coefficient of friction

  • Fg = Wsin()

  • So the block will slide when Wcos() = Wsin()

  • So

     = sin()/cos() = tan()

    The larger  is the larger  must be for the block to slide


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ISNS 4371 - Phenomena of Nature

Projectile Motion

The vertical and horizontal components of the motion of a projectile are independent of each other.

Vh = 0

Vh = v1

Vh = v2

Three projectiles fired with initial horizontal velocities of 0, v1, and v2 will all hit the ground at the same time.


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ISNS 4371 - Phenomena of Nature

Shoot the Monkey

(or The Monkey and the Coconut)

A monkey is on a branch in the air.

A hunter is on the ground some distance from the monkey.

He fires a gun at the instant the monkey drops from the tree.

Should he aim above or below the monkey?


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ISNS 4371 - Phenomena of Nature


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The monkey is 8 m in the air.

The hunter is 15 m from the spot on the ground directly below the monkey.

The muzzle velocity of the gun is 20 m/s.

So:

a = 8, b = 15

c2 = 64 + 225 = 289

c = 17

v = 20 m/s

The component of the bullet velocity in the horizontal direction is:

vh = 20 cos A = 20(b/c) = 20(15/17) = 300/17

The component of the bullet velocity in the vertical direction is:

vv = 20 sin A = 20(a/c) = 20(8/17) = 160/17

ISNS 4371 - Phenomena of Nature

B

c

a

A

C

b

c2 = a2 + b2

cos A = b/c

sin A = a/c


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ISNS 4371 - Phenomena of Nature

Horizontal distance of bullet (x) = vht

The time for the bullet to travel 15 m horizontally is:

t = x/vh = 15(17/160) = 0.85 s

The height of the monkey and the bullet must be the same after 0.85 s

Height of bullet (yb) = vvt - 1/2gt2

Height of monkey (ym) = 8 - 1/2gt2

ym = yb

vvt -1/2gt2 = 8 - 1/2gt2

vvt = 8

vvt = (160/17)*0.85 = 8

QED

With constant velocity:

d = vt

Under acceleration

d = 1/2at2

Total distance:

d = d0 + v0t + 1/2at2

h = h0 + v0t - 1/2gt2


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ISNS 4371 - Phenomena of Nature

Newton’s Third Law

A body subjected to a force reacts with an equal counter force to the applied force:

That is, action and reaction are equal and oppositely directed, but never act on the same body.

For every action (force), there is an equal and opposite reaction (force)


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ISNS 4371 - Phenomena of Nature

Examples of Action/Reaction

Swimming - your hands and the water

Walking - your feet and the ground

Driving - a car’s tires and the road

A bug and a car’s windshield

A falling object - the object and the earth

A person pulling a spring

A deflating balloon - the air rushing out and the balloon

Pushing on the wall - your hand and the wall

Rocket ship - expelled fuel and rocket


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ISNS 4371 - Phenomena of Nature

A Rifle and a Bullet

When a bullet is fired from a rifle, the rifle recoils due to the interaction between the bullet and the rifle.

The force the rifle exerts on the bullet is equal and opposite to the force the bullet exerts on the rifle.

But the acceleration of the bullet is much larger that the acceleration of the rifle - due to Newton’s 2nd law: a = F/m

The acceleration due to a force is inversely proportional to the mass.

The force on the rifle and the bullet is the same but the mass of the rifle is much larger than the the mass of the bullet so the acceleration of the rifle is much less than the acceleration of the bullet.


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ISNS 4371 - Phenomena of Nature

Tension

Consider a block being pulled by a rope. The person doing the pulling at one end of the rope is not in contact with the block, and cannot exert a direct force on the block. Rather a force is exerted on the rope, which transmits that force to the block. The force experienced by the block from the rope is called the stretching force, commonly referred to as tension.

Tension is actually not a force - tension transmits the stretching force. A force always has a direction - the tension in a string or rope must follow the rope! The tension may have to extend around corners, over and under pulleys, etc. So, tension transmits a force through a string or rope, but tension is not a force. Tension doesn't work exactly the way force does.


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ISNS 4371 - Phenomena of Nature

Suppose you hang a 5 Newton weight from a string, and hold the other end of the string in your hand. If the weight (and the string and your hand) is at rest, then the weight exerts a 5 N downward force on the lower end of the string, and you exert a 5 N upward force on the upper end of the string. What is the stretching force/tension in the string? It is possible to build very plausible arguments that the tension in the string is 10 N, or that it is 0 N, or that it is 5 N - but what is it, really, and why?

Remember - tension transmits the force. It would be the same as if you were holding the weight in your hand - the force on your hand would be 5 N. Therefore the stretching force/tension is 5 N.

In a tug-of-war, the tension in the rope is produced by the people pulling on opposite ends of the rope. The forces at either end of the rope are equal and opposite. What is the tension in the rope?

What happens if a 200 lb man wearing socks and a 100 lb girl wearing rubber-soled shoes have a tug-of-war? Who wins?


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ISNS 4371 - Phenomena of Nature

Momentum

Momentum is mass times velocity, a vector quantity:

Mom=mv

The more massive an object, the greater its momentum.

The greater the velocity of an object, the larger its momentum.

The momentum of an object is changed by applying a force:

- the larger the applied force, the greater the change in momentum.

- the longer the force is applied, the greater the change in momentum


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ISNS 4371 - Phenomena of Nature

Impulse

Impulse of a force is the force times the time over which the force acts on a body.

I = F x ∆T

∆ means a change in a quantity - ∆Tis the time over which the force is acting.

From Newton’s second law:

Therefore, an Impulse produces a change in momentum of a body.


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ISNS 4371 - Phenomena of Nature

  • Process of minimizing an impact force - approached from the definition of the impulse of force: If an impact stops a moving object, then the change in momentum is a fixed quantity, and extending the time of the collision will decrease the impact force by the same factor.

  • This principle is applied in many common-sense situations:

    • If you jump to the ground from any height, you bend your knees upon impact, extending the time of collision and lessening the impact force.

    • A boxer moves away from a punch, extending the time of impact and lessening the force.

    • Automobiles are made to collapse upon impact, extending the time of collision and lessening the impact force.

    • If you drop a glass on hard floor - it breaks. If you drop it on a soft carpet, the impact time is extended as the glass sinks into the carpet - impact force reduced - glass doesn’t break.


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