Answer:
x(t) = -8sin2t
Explanation:
See the attachment for solution
From my solving, we can deduce that w² = 4, and thus, w = 2
Therefore, the general solution is
x(t) = c1 cos2t + c2 sin2t
Considering the final variable, we can conclude that
x(0) = 0
x'(0) = -8 m/s
The final solution, thus
x(t) = -8sin2t
Answer:
The ball has an initial linear kinetic energy and initial rotational kinetic energy which can both be converted into gravitational potential energy. Therefore the hill with friction will let the ball reach higher.
Explanation:
The ball has an initial linear kinetic energy and initial rotational kinetic energy which can both be converted into gravitational potential energy. Therefore the hill with friction will let the ball reach higher.
This is because:
If we consider the ball initially at rest on a frictionless surface and a force is exerted through the centre of mass of the ball, it will slide across the surface with no rotation, and thus, there will only be translational motion.
Now, if there is friction and force is again applied to the stationary ball, the frictional force will act in the opposite direction to the force but at the edge of the ball that rests on the ground. This friction generates a torque on the ball which starts the rotation.
Therefore, static friction is infact necessary for a ball to begin rolling.
Now, from the top of the ball, it will move at a speed 2v, while the centre of mass of the ball will move at a speed v and lastly, the bottom edge of the ball will instantaneously be at rest. So as the edge touching the ground is stationary, it experiences no friction.
So friction is necessary for a ball to start rolling but once the rolling condition has been met the ball experiences no friction.
Answer:
True
Explanation:
Standard heat of formation is the heat change that deals with the formation of 1mole at standard rates and states of the given reactants . Standard heat of formation is the difference between the enthalpy change of reactants and products.
The idea behind capitalism is that the free market of products and ideas is owned and driven by private citizens. A capitalist society is a social order in which private property rights and the free market serve as the basis of trade, distribution of goods, and development.
