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ziro4ka [17]
3 years ago
6

What is the relationship between the center of gravity and the support base for an object that is in stable equilibrium?

Physics
1 answer:
Norma-Jean [14]3 years ago
8 0

Answer:

when the center of gravity is within the washing area, the torque returns in the body to its initial position and is in a stable equilibrium

Explanation:

The concept of center of gravity is equivalent to the concept of center of mass, in this place all external forces applied can be considered.

When we analyze the balance of a body that is the torque it is the one that defines the balance

      τ = F xd

If the torque tends to restore the body to the initial position the balance is stable, but if the torque has to increase the body's rotation the balance is unstable

. When the body tends to rotate the torque with respect to the pivot point at the base it decreases because the distance from the center of gravity to the end of the base decreases in value, but it has to return it to the initial position, the balance is stable. The critical point of this process is when the center of gravity is at the limit of the body base area in this case the torque is zero; If the body rotates a little more the center of gravity is outside the base, the torque changes sign and has to increase the turn, going to an unstable balance.

In summary, when the center of gravity is within the washing area, the torque returns in the body to its initial position and is in a stable equilibrium.

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Answer:

1)

When the person throws the ball away, the person rolls backward. This is due to the law of conservation of momentum: in fact, the total momentum of the person+ball system must be conserved.

At the beginning,

p_i=0

after throwing the ball, the total momentum is the sum of the momentum of the person and of the ball:

p_f=p_p + p_b

Since momentum is conserved,

p_i = p_f\\0=p_p+p_b

So

p_p = -p_b

Therefore, the person has equal momentum (in magnitude) but opposite direction to the ball, so the person rolls backward.

However, if the person hold to the ball, then they will have same momentum (moving in the same direction). In order to conserve the total momentum (which was zero at the beginning), the only possible solution is that

p_p=p_b=0

which means that both the person and the ball will remain at rest. This is because there are no external forces acting on the system, so the system cannot move.

2)

The change in momentum of an object is given by

\Delta p=m(v-u)

where

m is the mass of the object

v is its final velocity

u is the initial velocity

For the clay ball in this problem, we have:

m = 50 g = 0.050 kg

v = 0 m/s (it sticks on the wall)

u = 1 m/s

So its change in momentum is

\Delta p_c=(0.050)(0-1)=-0.050 kg m/s

For the superball, we have:

m = 50 g = 0.050 kg

v = -0.8 m/s (it bounces back)

u = 1 m/s

So its change in momentum is

\Delta p_s = (0.050)(-0.8-1)=-0.09 kg m/s

So, the superball has a greater change in momentum (in magnitude).

3a)

According to Newton's third law of motion:

"When an object A exerts a force (action force) on an object B, then object B exerts an equal and opposite force (reaction force) on object A".

Here, we have a Hummer and a Beetle colliding head-on: we can identify them as object A and object B. Therefore, according to Newton's third law:

- The action force is the force of impact exerted by the Hummer on the Beetle

- The reaction force is the force of impact exerted by the Beetle on the Hummer

And according to the Law, the two forces are equal in magnitude: so, the two vehicles experience the same force of impact.

3b)

The change in momentum of each vehicle during the collision can be written as

\Delta p = F\Delta t (1)

where

\Delta p is the change in momentum

F is the force experienced by the vehicle

\Delta t is the duration of the collision

in part 3a), we said that the two vehicles experience the same force in the collision.

Moreover, the duration of the collision, \Delta t, is the same for the two vehicles.

As a result, according to formula (1), the two vehicles have same change in momentum (however, the directions would be opposite, since they experience force in opposite directions).

3c)

According to Newton's second law of motion, the acceleration of an object is given by:

a=\frac{F}{m}

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F is the force experienced by the object

m is its mass

a is its acceleration

In part 3a), we stated that the force experienced by the Beetle and the Hummer is the same. However, the mass of the Beetle is smaller than the mass of the Hummer: from the equation we see that the acceleration is inversely proportional to the mass, therefore the Beetle will experience a greater acceleration.

4a)

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F=\frac{\Delta p}{\Delta t}

Where

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4b)

The force experienced by the climber if falling is given by

F=\frac{\Delta p}{\Delta t}

Where

F is the force experienced by the climber

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\Delta t is the duration of fall

Nylon is a very elastic material, so it is able to "soften" the fall by stretching a lot. As a result, the nylon increases the value of \Delta t in the formula. Since the force experienced by the climber is inversely proportional to \Delta t, the climber will feel less force thanks to the nylon.

4c)

This technique is used to exploit the "push" given by the second car of the train to the first car when the brakes are applied.

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