Riptide wrote:
Wow that was quick. Nice job! Sorry for not mentioning the pressure, you made the right assumption for keeping them the same. Your turn!
Alright. Nathan Chen is an 18-year-old American figure skater competing at the 2018 Winter Olympics. During one of his tricks, he begins spinning around at a steady 2π rad/s. Bringing his arms in toward his chest, Chen is able to decrease his moment of inertia by half. After doing this, how many revolutions does Chen complete after 3 seconds of spinning? Assume that because the ice is frictionless and that his angular velocity does not decrease.
By the conservation of angular momentum, Iw = Iw (of course assuming frictionless surfaces). When the moment of inertia is cut in half, the angular velocity doubles, resulting in a angular velocity of 4π rad/s. After 3 seconds, he has traveled 12π radians, or 6 revolutions (1 revolution = 2π yay unit circle).
Correct. Your turn!
Re: Hovercraft B/C
Posted: February 10th, 2018, 5:36 pm
by Riptide
Justin72835 wrote:
Riptide wrote:
Justin72835 wrote:
Alright. Nathan Chen is an 18-year-old American figure skater competing at the 2018 Winter Olympics. During one of his tricks, he begins spinning around at a steady 2π rad/s. Bringing his arms in toward his chest, Chen is able to decrease his moment of inertia by half. After doing this, how many revolutions does Chen complete after 3 seconds of spinning? Assume that because the ice is frictionless and that his angular velocity does not decrease.
By the conservation of angular momentum, Iw = Iw (of course assuming frictionless surfaces). When the moment of inertia is cut in half, the angular velocity doubles, resulting in a angular velocity of 4π rad/s. After 3 seconds, he has traveled 12π radians, or 6 revolutions (1 revolution = 2π yay unit circle).
Correct. Your turn!
Consider a satellite orbiting Earth elliptically. Find the ratio of its speed at perihelion to that at aphelion.
Re: Hovercraft B/C
Posted: February 10th, 2018, 8:47 pm
by Adi1008
Riptide wrote:
Justin72835 wrote:
Riptide wrote:
By the conservation of angular momentum, Iw = Iw (of course assuming frictionless surfaces). When the moment of inertia is cut in half, the angular velocity doubles, resulting in a angular velocity of 4π rad/s. After 3 seconds, he has traveled 12π radians, or 6 revolutions (1 revolution = 2π yay unit circle).
Correct. Your turn!
Consider a satellite orbiting Earth elliptically. Find the ratio of its speed at perihelion to that at aphelion.
[math]r_{a}/r_{p}[/math]
Re: Hovercraft B/C
Posted: February 10th, 2018, 9:01 pm
by Riptide
Adi1008 wrote:
Riptide wrote:
Justin72835 wrote:
Correct. Your turn!
Consider a satellite orbiting Earth elliptically. Find the ratio of its speed at perihelion to that at aphelion.
[math]r_{a}/r_{p}[/math]
Guess that was too easy. Your turn!
Re: Hovercraft B/C
Posted: February 11th, 2018, 10:51 am
by Adi1008
Riptide wrote:
Adi1008 wrote:
Riptide wrote:
Consider a satellite orbiting Earth elliptically. Find the ratio of its speed at perihelion to that at aphelion.
[math]r_{a}/r_{p}[/math]
Guess that was too easy. Your turn!
A 2kg rock is thrown straight downwards from a height of 10 meters with a velocity of 5 m/s. When it lands, it sinks 0.5 meters into the snow below. What is the average force between the rock and the snow as the rock is sinking?
Re: Hovercraft B/C
Posted: February 11th, 2018, 1:31 pm
by Justin72835
Adi1008 wrote:
Riptide wrote:
Adi1008 wrote:
[math]r_{a}/r_{p}[/math]
Guess that was too easy. Your turn!
A 2kg rock is thrown straight downwards from a height of 10 meters with a velocity of 5 m/s. When it lands, it sinks 0.5 meters into the snow below. What is the average force between the rock and the snow as the rock is sinking?
The combined mechanical energy of the system is found by adding its initial kinetic and potential energy, which gives 221 J.
Since it travels a distance of 0.5 meters when slowing down, you can use Fd = W, which gives 442 N as the net force acting on the object. Now you can set up a net force equation: Fnet = Fsnow - Fg, where Fsnow = 461.6 N.
Final Answer: 461.6 N
Re: Hovercraft B/C
Posted: February 11th, 2018, 6:49 pm
by Adi1008
Justin72835 wrote:
Adi1008 wrote:
Riptide wrote:
Guess that was too easy. Your turn!
A 2kg rock is thrown straight downwards from a height of 10 meters with a velocity of 5 m/s. When it lands, it sinks 0.5 meters into the snow below. What is the average force between the rock and the snow as the rock is sinking?
The combined mechanical energy of the system is found by adding its initial kinetic and potential energy, which gives 221 J.
Since it travels a distance of 0.5 meters when slowing down, you can use Fd = W, which gives 442 N as the net force acting on the object. Now you can set up a net force equation: Fnet = Fsnow - Fg, where Fsnow = 461.6 N.
Final Answer: 461.6 N
Looks good to me; your turn!
Re: Hovercraft B/C
Posted: February 12th, 2018, 1:56 pm
by Justin72835
Adi1008 wrote:
Looks good to me; your turn!
A ball of mass 3kg is suspended from a 20m long massless rope. A spherical bullet of mass 50g is fired at the ball with a velocity of 450m/s and they collide elastically. Determine the angle formed by the rope and vertical once the ball has reached its maximum height.
Re: Hovercraft B/C
Posted: February 12th, 2018, 2:41 pm
by Riptide
Justin72835 wrote:
Adi1008 wrote:
Looks good to me; your turn!
A ball of mass 3kg is suspended from a 20m long massless rope. A spherical bullet of mass 50g is fired at the ball with a velocity of 450m/s and they collide elastically. Determine the angle formed by the rope and vertical once the ball has reached its maximum height.
Since this is an elastic collision, the velocity of the ball after the collision is 2m1/(m1+m2)*v1, resulting in a velocity 14.8 m/s. Using the conservation of energy, we get a change in height of 11.1 meters. Drawing a diagram of this makes it easy to solve for the angle, which is 63.6 degrees.
Re: Hovercraft B/C
Posted: February 12th, 2018, 2:43 pm
by Justin72835
Riptide wrote:
Justin72835 wrote:
Adi1008 wrote:
Looks good to me; your turn!
A ball of mass 3kg is suspended from a 20m long massless rope. A spherical bullet of mass 50g is fired at the ball with a velocity of 450m/s and they collide elastically. Determine the angle formed by the rope and vertical once the ball has reached its maximum height.
Since this is an elastic collision, the velocity of the ball after the collision is 2m1/(m1+m2)*v1, resulting in a velocity 14.8 m/s. Using the conservation of energy, we get a change in height of 11.1 meters. Drawing a diagram of this makes it easy to solve for the angle, which is 63.6 degrees.