Find how much a wire stretched at the bottom of swing of pendulum

[rezihk]

1. A building is to be demolished by a 400kg shell ball swinging on the end of a 30.0 m steel wire of diameter 5.00 cm hanging from a tall crane. As the ball is swung though an arc from side to side, the wire makes an angle of 50° with the vertical at the top of the swing. find the amount by which the wire is stretched at the bottom of the swing



2. stress=F/A, strain=ΔL/L, F=ma, Y= Young's Modulus



3. ΔL=F/A*L/Y

 

[vivekrai]

I suppose you have the problem at finding the force. User Energy conservation to find the velocity at the lowermost point. Then use the equation T-mg = mv^2/(L+ΔL)

 

[issacnewton]

vivek, let the guy show some work at least. that's the forum policy. the person has not shown ANY work.

 

[rezihk]

i figured out all these values and plugged them into the eqn i have:

A=1.96E-3 m^2 wire
Y=20E10
L=30m
Tension if it were at rest and bottom: T=mg=3924N
and got dL=0.03cm
but I'm assuming at it stretches the same if it were at rest or accelerating when at the bottom
how do i take acceleration into account?

 

[asteriatic]

[/b]

I would approach this problem by first determining the relevant equations and principles that can be applied to solve it. In this case, we can use the equations for stress and strain, as well as the relationship between force, mass, and acceleration. We can also use the concept of Young's Modulus, which is a measure of a material's stiffness and can be used to calculate the amount of stretch in a material under a given force.

Using the given information, we can calculate the force (F) acting on the wire by multiplying the mass (m) of the shell ball by the acceleration (a) due to gravity (9.8 m/s^2). This gives us a force of 3920 N.

Next, we can determine the cross-sectional area (A) of the wire by using the formula for the area of a circle (A=πr^2) with the given diameter of 5.00 cm. This gives us an area of 0.0019635 m^2.

Using the angle of 50° at the top of the swing, we can find the length (L) of the wire using trigonometry. This gives us a length of 30.6 m.

Now, we can plug these values into the equation for strain (ΔL/L) and solve for the change in length (ΔL) at the bottom of the swing.

ΔL=F/A*L/Y = (3920 N)/(0.0019635 m^2)*(30.6 m)/(200 x 10^9 Pa) = 9.83 x 10^-4 m = 0.983 mm

Therefore, the wire will be stretched by approximately 0.983 mm at the bottom of the swing. This information can be useful in determining the strength and durability of the wire and ensuring it can withstand the force of the swinging shell ball.