tommy builds a human sling shot that has an elastic constant of 4000 N/m. He puts his little sister in it and pulls it back for 5 meters. How much energy does his 25 kg sister have as she leaves the sling shot and how fast is she flying?
The stored potential energy in the elastic material is (1/2)kX^2 = 50,000 J. That gets converted to kinetic energy when the sister is released.
Set (M/2)V^2 = 50,000 J and solve for V.
The answer I get is too fast to be safe.
No i'm pretty sure you are right, thank you!!!
To determine the energy and velocity of Tommy's sister as she leaves the sling shot, we can use the principle of conservation of mechanical energy, which states that the total mechanical energy of a system remains constant if no external forces act upon it.
The total mechanical energy of the system includes both potential energy (due to the elastic potential energy stored in the sling shot) and kinetic energy (as Tommy's sister flies through the air). The equation for mechanical energy is:
E = PE + KE
where:
E = mechanical energy
PE = potential energy
KE = kinetic energy
First, we need to calculate the potential energy (PE) stored in the sling shot when it is pulled back by 5 meters. The formula for potential energy in a spring is:
PE = 0.5 * k * x²
where:
k = elastic constant
x = displacement
Substituting the given values into the formula:
PE = 0.5 * 4000 N/m * (5 m)²
PE = 0.5 * 4000 N/m * 25 m²
PE = 0.5 * 4000 N/m * 625 m²
PE = 0.5 * 4000 N/m * 625 m²
PE = 0.5 * 2,500,000 N
PE = 1,250,000 J
Now, we need to consider the relationship between potential energy and kinetic energy when Tommy's sister leaves the sling shot. According to the principle of conservation of mechanical energy, the potential energy will be transformed into kinetic energy, given that no external forces act on the system. So, the kinetic energy (KE) will be equal to the potential energy (PE).
Therefore, KE = 1,250,000 J
Finally, we can determine the velocity (v) of Tommy's sister using the kinetic energy formula:
KE = 0.5 * m * v²
where:
m = mass
v = velocity
Rearranging the equation to solve for velocity:
v² = (2 * KE) / m
v² = (2 * 1,250,000 J) / 25 kg
v² = 100,000 J / kg
v² = 40,000 m²/s²
Taking the square root of both sides:
v ≈ √40,000 m²/s²
v ≈ 200 m/s
Therefore, Tommy's sister will have approximately 1,250,000 J of energy and will be flying at a speed of approximately 200 m/s as she leaves the sling shot.