Spider silk is a remarkable elastic material. A particular strand has spring constant 70 mM/m, and it stretches 9.5 cm when a fly hits it. How much work did the fly's impact do on the silk strand?
work= 1/2 k x^2= 1/2 .07N/m*.095^2 m^2= you do it.
mM/m is not an appropriate dimension for a spring constant. What is it supposed to mean?
it is 0.07N/m
To determine the work done by the fly's impact on the silk strand, we need to use the formula for work:
Work = (1/2) * k * x²
Where:
k is the spring constant, and
x is the displacement of the spring (in this case, the stretch of the silk strand).
Let's calculate the work done step by step:
Step 1: Convert the spring constant to the correct units.
The given spring constant is 70 mM/m. We need to convert this to N/m (Newtons per meter) for our calculation. Since 1 m = 1000 mm, we can convert mM/m to N/m by multiplying by 0.001:
70 mM/m * 0.001 = 0.07 N/m
Step 2: Convert the stretch displacement to meters.
The given stretch displacement is 9.5 cm. We need to convert this to meters to match the units of the spring constant. Since 1 m = 100 cm, we can convert cm to meters by multiplying by 0.01:
9.5 cm * 0.01 = 0.095 m
Step 3: Plug the values into the formula for work.
Work = (1/2) * k * x²
Work = (1/2) * 0.07 N/m * (0.095 m)²
Calculating the equation, we have:
Work = 0.5 * 0.07 N/m * (0.009025 m²)
Work = 0.000315875 N * m
Step 4: Simplify the units.
The unit for work is Joules (J), so we need to convert the product of force (N) and displacement (m) to Joules. Since 1 N * m = 1 J, we can express the work as:
Work = 0.000315875 J
Therefore, the fly's impact did approximately 0.000315875 Joules of work on the silk strand.