To solve this problem it is necessary to apply the rules and concepts related to logarithmic operations.
From the definition of logarithm we know that,
In this way for the given example we have that a logarithm with base 10 expressed in the problem can be represented as,
We can express this also as,
By properties of the logarithms we know that the logarithm of a power of a number is equal to the product between the exponent of the power and the logarithm of the number.
So this can be expressed as
Since the definition of the base logarithm 10 of 10 is equal to 1 then
The value of the given logarithm is equal to 6
The force applied on the spring to stretch it is 13.2 N.
Hooke's law is a law of elasticity discovered by the English scientist Robert Hooke in 1660 that states that the displacement or size of a deformation is directly proportional to the deforming force or load for relatively small deformations of an object. When the load is removed under these conditions, the object returns to its original shape and size.
According to Hooke's law, F = k*e
where F is the force on the spring
k is force constant
and e is extension
F = (110)*(0.12)
F = 13.2 N
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We actually don't need to know how far he/she is standing from the net, as we know that the ball reaches its maximum height (vertex) at the net. At the vertex, it's vertical velocity is 0, since it has stopped moving up and is about to come back down, and its displacement is 0.33m. So we use v² = u² + 2as (neat trick I discovered just then for typing the squared sign: hold down alt and type 0178 on ur numpad wtih numlock on!!!) ANYWAY....... We apply v² = u² + 2as in the y direction only. Ignore x direction.
IN Y DIRECTION: v² = u² + 2as 0 = u² - 2gh u = √(2gh) (Sub in values at the very end)
So that will be the velocity in the y direction only. But we're given the angle at which the ball is hit (3° to the horizontal). So to find the velocity (sum of the velocity in x and y direction on impact) we can use: sin 3° = opposite/hypotenuse = (velocity in y direction only) / (velocity) So rearranging, velocity = (velocity in y direction only) / sin 3° = √(2gh)/sin 3° = (√(2 x 9.8 x 0.33)) / sin 3° = 49 m/s at 3° to the horizontal (2 sig figs)
Answer:
W= 210 N
Explanation:
Just use work = Fparallel*d
W= 35*6
W= 210 N
