A trebuchet -- that uses a weight of 24.95 kg from a distance of 0.7 m upwards -- launches a projectile with a weight of 0.2 kg. Then what is the acceleration of the projectile?
Help, my brain doesn't seem to wrap around this
To find the acceleration of the projectile launched by the trebuchet, we can use the principles of conservation of energy and Newton's second law.
First, let's determine the potential energy of the weight before it is released. The potential energy is given by the equation:
Potential Energy = mass * gravity * height
In this case, the mass of the weight is 24.95 kg, gravity is approximately 9.8 m/s², and the height is 0.7 m. Thus, the potential energy is:
Potential Energy = 24.95 kg * 9.8 m/s² * 0.7 m = 169.1219 J
Since the potential energy is converted into the kinetic energy of the projectile, we can equate the potential energy to the kinetic energy to find the velocity of the projectile just as it leaves the trebuchet:
Kinetic Energy = (1/2) * mass * velocity^2
The kinetic energy is given by the weight of the projectile and the velocity of the projectile is what we are trying to find. The mass of the projectile is 0.2 kg. So, we have:
Kinetic Energy = (1/2) * 0.2 kg * velocity^2
Since the weight is launched upwards, the velocity of the projectile is positive. Rearranging the equation, we get:
velocity = √(2 * Kinetic Energy / mass)
Substituting the given values:
velocity = √(2 * 169.1219 J / 0.2 kg) ≈ 184.90 m/s
Now, we have found the initial velocity of the projectile as it leaves the trebuchet.
To calculate the acceleration of the projectile, we can use Newton's second law, which states that the force acting on an object is equal to its mass multiplied by its acceleration:
Force = mass * acceleration
In this case, the force acting on the projectile is its weight, which is given by:
Force = mass * gravity
Substituting the values:
0.2 kg * 9.8 m/s² = 1.96 N
Since the only force acting on the projectile is its weight, and it moves in the vertically upward direction, the acceleration can be calculated using Newton's second law:
1.96 N = 0.2 kg * acceleration
Rearranging the equation to solve for acceleration:
acceleration = 1.96 N / 0.2 kg ≈ 9.8 m/s²
Therefore, the acceleration of the projectile launched by the trebuchet is approximately 9.8 m/s².