A 1.0 kg puck sliding at 15 m/s along some horizontal frictionless ice strikes and compresses a horizontal spring attached to one end of the ice rink. If the spring has a constant of 35 N/m, what is the maximum compression of the spring?
Hey, you have done several of these now. Try
is this a conservation problem?
i don't know if should use , 1/2mv^2=kx to solve it or not
(1/2) m v^2 = (1/2) k x^2
To find the maximum compression of the spring, we need to analyze the energy conservation in the system.
When the puck strikes the spring and compresses it, the kinetic energy of the puck is converted into potential energy stored in the compressed spring. At the maximum compression point, all of the puck's initial kinetic energy is converted into potential energy.
The equation for potential energy stored in a spring is given by:
Potential energy = (1/2) * k * x^2
where k is the spring constant and x is the displacement or compression of the spring.
In this case, the initial kinetic energy of the puck is given by:
Initial kinetic energy = (1/2) * mass * velocity^2
Let's calculate the initial kinetic energy:
Initial kinetic energy = (1/2) * 1.0 kg * (15 m/s)^2 = 112.5 J
Now, equating the initial kinetic energy to the potential energy stored in the spring at maximum compression:
112.5 J = (1/2) * 35 N/m * x^2
Simplifying the equation, we can find the maximum compression:
112.5 J = 17.5 N/m * x^2
Dividing both sides of the equation by 17.5 N/m:
x^2 = 6.4286 m^2
Taking the square root of both sides gives us:
x = √6.4286 m ≈ 2.54 m
Therefore, the maximum compression of the spring is approximately 2.54 meters.