I need help on 11 - 14
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<h2>Right answer: acceleration due to gravity is always the same </h2><h2 />
According to the experiments done and currently verified, in vacuum (this means there is not air or any fluid), all objects in free fall experience the same acceleration, which is <u>the acceleration of gravity</u>.
Now, in this case we are on Earth, so the gravity value is
Note the objects experience the acceleration of gravity regardless of their mass.
Nevertheless, on Earth we have air, hence <u>air resistance</u>, so the afirmation <em>"Free fall is a situation in which the only force acting upon an object is gravity" </em>is not completely true on Earth, unless the following condition is fulfiled:
If the air resistance is <u>too small</u> that we can approximate it to <u>zero</u> in the calculations, then in free fall the objects will accelerate downwards at and hit the ground at approximately the same time.
The initial kinetic energy of the cart is
(1)
where m is the mass of the cart and v its initial velocity.
Then, the cart hits the spring compressing it. The maximum compression occurs when the cart stops, and at that point the kinetic energy of the cart is zero, so all its initial kinetic energy has been converted into elastic potential energy of the spring:
where k is the spring constant and x is the spring compression.
For energy conservation, K=U. We can calculate U first: the compression of the spring is x=60 cm=0.60 m, while the spring constant is k=250 N/m, so
So, the initial kinetic energy of the cart is also 45 J, and from (1) we can find the value of the initial velocity:
where m is the mass of the cart and v its initial velocity.
Then, the cart hits the spring compressing it. The maximum compression occurs when the cart stops, and at that point the kinetic energy of the cart is zero, so all its initial kinetic energy has been converted into elastic potential energy of the spring:
where k is the spring constant and x is the spring compression.
For energy conservation, K=U. We can calculate U first: the compression of the spring is x=60 cm=0.60 m, while the spring constant is k=250 N/m, so
So, the initial kinetic energy of the cart is also 45 J, and from (1) we can find the value of the initial velocity: