A catapult with a spring constant of 1.0 104 newtons per meter is required to launch an airplane from the deck of an aircraft carrier. The plane is released when it has been displaced 0.50 meter from its equilibrium position by the catapult. What is the energy acquired by the airplane from the catapult during takeoff
0.50 m is presumably how far the spring is pulled back, not the displacement when the airplane leaves the catapult.
In this case, the energy acquired is (1/2) k X^2
k = 1.0*10^4 N/m
X = -.50 m
The answer will be in Joules
Fs=-kx
Fs=-(1.0x10^4 N/m)(-0.50 m)
Fs= 5,000 N
W=1/2k(xi^2-xf^2)
W=1/2(1.0x10^4 N/m)[(0m)^2 -(-0.50m)^2]
W= 1,250 J
That's my answer but I'm not really sure if it's correct
Well, launching an airplane from an aircraft carrier is no joke! But let's calculate the energy acquired by the airplane.
The energy acquired by the airplane can be calculated using the formula for elastic potential energy, which is given by:
E = (1/2) k x^2
Where:
E is the energy acquired by the airplane
k is the spring constant
x is the displacement of the airplane from its equilibrium position
Given:
k = 1.0 × 10^4 N/m (spring constant)
x = 0.50 m (displacement of the airplane)
Let's plug in the values and calculate:
E = (1/2) × (1.0 × 10^4 N/m) × (0.50 m)^2
E = (1/2) × (1.0 × 10^4 N/m) × (0.25 m^2)
E = 1250 Joules
So, the energy acquired by the airplane from the catapult during takeoff is 1250 Joules. That's quite an energetic launch!
To calculate the energy acquired by the airplane from the catapult during takeoff, we can use the formula for potential energy stored in a spring:
Potential energy (U) = 0.5 * k * x^2
where k is the spring constant and x is the displacement from the equilibrium position.
In this case, the spring constant (k) is given as 1.0 * 10^4 N/m, and the displacement (x) is 0.50 meters.
Substituting the given values into the formula, we get:
Potential energy (U) = 0.5 * (1.0 * 10^4 N/m) * (0.50 m)^2
Calculating further:
U = 0.5 * (1.0 * 10^4) * (0.50)^2
U = 0.5 * 10^4 * 0.25
U = 0.125 * 10^4
U = 1250 Joules
Therefore, the energy acquired by the airplane from the catapult during takeoff is 1250 Joules.
To find the energy acquired by the airplane from the catapult during takeoff, we need to calculate the potential energy stored in the spring.
The potential energy stored in a spring can be given by the formula:
E = (1/2)kX^2
Where:
E is the potential energy
k is the spring constant
X is the displacement from equilibrium position
In this case, the spring constant (k) is given as 1.0 × 10^4 N/m and the displacement (X) is given as 0.50 m.
Let's substitute these values into the formula to calculate the potential energy acquired by the airplane:
E = (1/2) * (1.0 × 10^4 N/m) * (0.50 m)^2
Now, let's solve the equation:
E = (1/2) * (1.0 × 10^4 N/m) * (0.25 m^2)
= 1.25 × 10^3 J
Therefore, the energy acquired by the airplane from the catapult during takeoff is 1.25 × 10^3 Joules.