Answer:
The ratio m_2/m_1 of the masses is 9.745
Explanation:
Formula for frequency when mass m_1 is hung on the spring:
where:
k is the spring constant
Formula for frequency when mass m_2 is hung on the spring along with m_1:
where:
k is the spring constant.
In order to find ratio m_2/m_1, Divide the above equations:
On Solving the above equation:
The ratio m_2/m_1 of the masses is 9.745
Answer: Total work done on the block is 3670.5 Joules.
Step by step:
Work done:
With F the force, d the displacement, and theta the angle of action (which is 0 since the block is pushed along the direction of displacement, and cos 0 = 1)
Given:
F = 75 N
m = 31.8 kg
Final velocity
In order to calculate the Work we need to determine the displacement, or distance the block travels. We can use the information about F and m to first figure out the acceleration:
Now we can determine the displacement from the following formula:
Here, the initial displacement is 0 and initial velocity is also 0 (at rest):
Now we still have "t" as unknown. But we are given one more bit of information from which this can be determined:
(using vf as final velocity, and tf as final time)
So it takes about 6.44 seconds for the block to move. This allows us to finally calculate the displacement:
and the corresponding work: