Energy & Momentum Calculations Assessment
Answer the following questions.
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?
Ek=(1/2)mv²
Ep=(1/2)(KΔx)²
If spring has no mass,
equate Ek and Ep to solve for Δx.
To determine the maximum compression of the spring, you need to use the principles of conservation of energy and momentum.
Step 1: Calculate the initial kinetic energy of the puck.
The initial kinetic energy of an object can be calculated using the formula: KE = (1/2)mv^2, where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.
In this case, the mass of the puck is given as 1.0 kg, and the velocity is given as 15 m/s.
So, the initial kinetic energy (KE) = (1/2)(1.0 kg)(15 m/s)^2.
Step 2: Calculate the potential energy stored in the spring.
When the puck compresses the spring, the kinetic energy is converted into potential energy stored in the spring. The potential energy stored in a spring can be calculated using the formula: PE = (1/2)kx^2, where PE is the potential energy, k is the spring constant, and x is the compression or displacement of the spring from its equilibrium position.
In this case, the spring constant is given as 35 N/m.
Since the spring is compressed, the displacement x has a negative value.
So, the potential energy (PE) = - (1/2)(35 N/m)(x)^2.
Step 3: Equate the initial kinetic energy to the potential energy stored in the spring.
According to the principle of conservation of energy, the initial kinetic energy of the puck is equal to the potential energy stored in the spring at maximum compression.
Therefore, we can write the equation: (1/2)(1.0 kg)(15 m/s)^2 = - (1/2)(35 N/m)(x)^2.
Step 4: Solve for x, the maximum compression of the spring.
Rearrange the equation to solve for x: (x)^2 = (2)(1/2)(1.0 kg)(15 m/s)^2 / (35 N/m).
Then calculate the square root of both sides to find the value of x: x = √[(2)(1/2)(1.0 kg)(15 m/s)^2 / (35 N/m)].
By performing the above calculations, you can determine the maximum compression of the spring.