The total mechanical energy of the system at any time t is the sum of the kinetic energy of motion of the ball and the elastic potential energy stored in the spring:
where m is the mass of the ball, v its speed, k the spring constant and x the displacement of the spring with respect its rest position.
Since it is a harmonic motion, kinetic energy is continuously converted into elastic potential energy and vice-versa.
When the spring is at its maximum displacement, the elastic potential energy is maximum (because the displacement x is maximum) while the kinetic energy is zero (because the velocity of the ball is zero), so in this situation we have:
Instead, when the spring crosses its rest position, the elastic potential energy is zero (because x=0) and therefore the kinetic energy is at maximum (and so, the ball is at its maximum speed):
Since the total energy E is always conserved, the maximum elastic potential energy should be equal to the maximum kinetic energy, and so we can find the value of the maximum speed of the ball:
Answer:
1. Potential hazard
2. Mining opportunity
Explanation:
The two reason, why astronomers are so interested in the discovery of additional Earth-approaching asteroids:
1. Potential hazard: We have proof that the dinosaurs got extinct because of an asteroid/comet strike on Earth. Also we have seen the effects of the Tunguska event and Chelyabinsk tragedy. These are enough to show us that asteroids can be very dangerous and wipe out the life from Earth.
2. Mining Opportunity: We have discovered a lot of asteroids which contains a lot of metal and precious elements. There can be a possibility of mining such asteroids in the future and reducing the burden on Earth.
Answer:
T = 1.766(M-m) Nm where M and m are the 2 masses of the objects
Explanation:
Let m and M be the masses of the 2 objects and M > m so the system would produce torque and rotational motion on the pulley. Force of gravity that exert on each of the mass are mg and Mg. Since Mg > mg, the net force on the system is Mg - mg or g(M - m) toward the heavier mass.
Ignore friction and string mass, and let g = 9.81 m/s2, the net torque on the pulley is the product of net force and arm distance to the pivot point, which is pulley radius r = 0.18 m
T = Fr = g(M - m)0.18 = 0.18*9.81(M - m) = 1.766(M-m) Nm
Answer and explanation;
According to twin studies attitudes may be genetically based, research has supported that Identical twins are more likely to share similar attitudes. Attitudes change as the result of behavior and not the other way around
Genetic factors may influence general dispositions and condition-ability that may influence formation of more specific attitudes. Controlled twin studies in US and Sweden reveal that identical twins share more similar attitudes than fraternal twins.
Answer:
2.64 m/s
Explanation:
Given that a 600 kilogram great "yellow" shark swimming to the right at a speed of 3 meters traveled each second as it tries to get lunch. An unsuspecting 100 kilogram blue fin tuna is minding its own business swimming to the left at a speed of 0.5 meters traveled each second. GULP! After the great "yellow" shark "collides" with the blue fin tuna
Momentum = MV
Momentum of the yellow shark before collision = 600 × 3 = 1800 kgm/s
Momentum of the tun final before collision = 100 × 0.5 = 50 kgm/s
Total momentum before collision = 1800 + 50 = 1850 kgm/s
Let's assume that they move together after collision. Then,
1850 = ( 600 + 100 ) V
1850 = 700V
V = 1850 / 700
V = 2.64285 m/s
Therefore, the momentum of the shark after collision is 2.64 m/ s approximately