Use the law of universal gravitation, which says the force of gravitation between two bodies of mass <em>m</em>₁ and <em>m</em>₂ a distance <em>r</em> apart is
<em>F</em> = <em>G m</em>₁ <em>m</em>₂ / <em>r</em>²
where <em>G</em> = 6.67 x 10⁻¹¹ N m²/kg².
The Earth has a radius of about 6371 km = 6.371 x 10⁶ m (large enough for a pineapple on the surface of the earth to have an effective distance from the center of the Earth to be equal to this radius), and a mass of about 5.97 x 10²⁴ kg, so the force of gravitation between the pineapple and the Earth is
<em>F</em> = (6.67 x 10⁻¹¹ N m²/kg²) (1 kg) (5.97 x 10²⁴ kg) / (6.371 x 10⁶ m)²
<em>F</em> ≈ 9.81 N
Notice that this is roughly equal to the weight of the pineapple on Earth, (1 kg)<em>g</em>, where <em>g</em> = 9.80 m/s² is the magnitude of the acceleration due to gravity, so that [force of gravity] = [weight] on any given planet.
This means that on this new planet with twice the radius of Earth, the pineapple would have a weight of
<em>F</em> = <em>G m</em>₁ <em>m</em>₂ / (2<em>r</em>)² = 1/4 <em>G m</em>₁ <em>m</em>₂ / <em>r</em>²
i.e. 1/4 of the weight on Earth, which would be about 2.45 N.
Answer:
Explanation:
Angular acceleration is defined by
Angular velocity is related to the period by
Putting all together:
Taking our initial (i) point now and our final (f) point one year later, we would have:
So for our values we have:
Where the minus sign indicates it is decelerating.
Answer:
<h2>The angular velocity just after collision is given as</h2><h2>
</h2><h2>At the time of collision the hinge point will exert net external force on it so linear momentum is not conserved</h2>
Explanation:
As per given figure we know that there is no external torque about hinge point on the system of given mass
So here we will have
now we can say
so we will have
Linear momentum of the system is not conserved because at the time of collision the hinge point will exert net external force on the system of mass
So we can use angular momentum conservation about the hinge point
Answer:
The force that cause the centripetal acceleration is the static friction, and the briefcase begin to move if the force of centripetal acceleration exceeds the force due to the static friction
Explanation:
Given data:
r = radius = 54.5 m
v = speed of the car = 12.4 m/s
The force due to the static friction that is exerted on the curve in the road is what causes the centripetal acceleration. If the force due to centripetal acceleration is greater than the force of static friction, then the briefcase will begin to roll.