A 2.13-kg object on a frictionless horizontal track is attached to the end of a horizontal spring whose force constant is 5.00 N
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The ball's vertical velocity at the time it just passes over the goal is 0 m/s. Its initial vertical velocity is unknown and we denote it by , where
here is the ball's initial speed. Vertically, the only force acting on the ball is gravity, which attributes a downward acceleration of 9.8 m/s^2. We expect the maximum height achieved by the ball to be 2.4 m, so we can find the initial speed by solving
The characteristics of the speed of the traveling waves allows to find the result for the tension in the string is:
T = 10 N
The speed of a wave on a string is given by the relationship.
v =
Where v es the velocty, t is the tension ang μ is the lineal density.
They indicate that the length of the string is L = 2.28 m and the pulse makes 4 trips in a time of t = 0.849 s, since the speed of the pulse in the string is constant, we can use the uniform motion ratio, where the distance traveled e 4 L
v =
v =
v =
v = 10.7 m / s
Let's find the linear density of the string, which is the length of the mass divided by its mass.
μ =
μ = 8.77 10⁻² kg / m
The tension is:
T = v² μ
Let's calculate
T = 10.7² 8.77 10⁻²
T = 1 0 N
In conclusion using the characteristics of the velocity of the traveling waves we can find the result for the tension in the string is:
T = 10 N
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The amount of energy needed to increase the temperature of a substance by 
is given by
where
m is the mass of the substance
is its specific heat capacity
is the increase in temperature
The water volume is
, since its density is 
, the mass of this sample of water is
The water specific heat capacity is
and the increase in temperature is
Therefore, the amount of energy needed is
where
m is the mass of the substance
The water volume is
The water specific heat capacity is
and the increase in temperature is
Therefore, the amount of energy needed is