A solid steel cylinder is standing (on one of its ends) vertically on the floor. The length of the cylinder is 3.4 m and its radius is 58 cm. When an object is placed on top of the cylinder, the cylinder compresses by an amount of 5.9 10-7 m. What is the weight of the object?
To find the weight of the object, we need to analyze the compression of the cylinder caused by the object's weight.
First, let's calculate the cross-sectional area of the cylinder's base. The base of the cylinder is circular, and its radius is given as 58 cm. We can use the formula for the area of a circle to find the cross-sectional area (A):
A = π * r^2
Where A is the cross-sectional area and r is the radius. Converting the radius to meters, we have r = 0.58 m. Plugging in the values:
A = π * (0.58 m)^2
Next, we can calculate the change in the volume of the cylinder caused by the compression. The change in volume (∆V) is given by the formula:
∆V = A * ∆h
Where ∆h is the change in height (compression) and A is the cross-sectional area. Plugging in the values:
∆V = A * ∆h
Now, let's find the weight of the object using the formula for weight (W):
W = m * g
Where W is the weight, m is the mass, and g is the acceleration due to gravity. We can rewrite this formula as:
m = W / g
To find the weight of the object, we need to know the mass. We can calculate the change in volume (∆V) caused by the compression and then determine the corresponding change in mass (∆m). Finally, the weight of the object can be found using:
W = g * ∆m
Now, let's put these steps together to find the weight of the object:
1. Calculate the cross-sectional area of the cylinder's base:
A = π * (0.58 m)^2
2. Calculate the change in volume caused by the compression:
∆V = A * ∆h
3. Determine the change in mass:
∆m = ρ * ∆V
Where ρ is the density of steel. The density of steel is approximately 7850 kg/m^3.
4. Calculate the weight of the object:
W = g * ∆m
Where g is the acceleration due to gravity, which is approximately 9.8 m/s^2.
By following these steps, you can find the weight of the object placed on top of the cylinder.