You drop a block from rest. The block lands on the spring (spring constant = 160Nm) and compresses it .5 m before the block and spring momentarilty come to rest. (The spring then pushes the block upward.) What is the mass of the block?
If needed, g=10ms2.
8kg
To find the mass of the block, we can use the principle of conservation of energy. The potential energy gained by compressing the spring is equal to the potential energy lost by the block while falling.
First, let's calculate the potential energy lost by the block while falling. We can use the formula:
Potential energy (PE) = m * g * h
where m is the mass of the block, g is the acceleration due to gravity (given as 10 m/s^2), and h is the height from which the block falls.
Since the block dropped from rest, it initially has no height. Therefore, the initial potential energy is zero.
Next, let's calculate the potential energy gained by compressing the spring. The potential energy of a spring is given by:
Potential energy (PE) = (1/2) * k * x^2
where k is the spring constant (given as 160 N/m) and x is the displacement of the spring (0.5 m).
Now we can set up an equation using the conservation of energy principle:
PE lost by block while falling = PE gained by compressing the spring
m * g * h = (1/2) * k * x^2
Since the block comes to rest momentarily after compressing the spring, there is no net spring potential energy at that moment. Therefore, the potential energy on both sides of the equation should be zero.
0 = (1/2) * k * x^2
Substituting the given values, we get:
0 = (1/2) * (160 N/m) * (0.5 m)^2
0 = 20 N * 0.25 m^2
0 = 5 N * m^2
Since we have zero on one side of the equation, the only possibility is that the mass of the block is zero.
Therefore, based on the given information, the mass of the block cannot be determined.