Robin Hood exerted an average force of 100 N in pulling back his bow by 0.5 m. He fired the arrow of mass 0.2 kg vertically upwards.
How much energy was stored in his bow?
How high did the arrow go?
BowEnergy=force*distance=100*.5=500N
PE at top=initial bow energy
mgh=500N
m=.2kg
g=9.8
now solve for height h.
ans
To find the energy stored in Robin Hood's bow, we can use the formula for elastic potential energy:
Elastic Potential Energy = (1/2) * k * x^2
where k is the force constant (also known as the spring constant) and x is the displacement.
In this case, the force applied by Robin Hood in pulling back his bow is 100 N, and the displacement is 0.5 m. Therefore, we need to calculate the force constant:
Force Constant (k) = Force (F) / Displacement (x)
= 100 N / 0.5 m
= 200 N/m
Now we can calculate the energy stored in the bow:
Elastic Potential Energy = (1/2) * k * x^2
= (1/2) * 200 N/m * (0.5 m)^2
= 50 J
Therefore, the energy stored in Robin Hood's bow is 50 J.
To find how high the arrow goes, we can use the principle of conservation of mechanical energy. At the highest point, all the initial kinetic energy will be converted into potential energy.
Initial kinetic energy = (1/2) * mass * velocity^2
In this case, the mass of the arrow is 0.2 kg. Since the arrow is fired vertically upwards, we know that the final velocity will be 0 m/s at the highest point.
Therefore, the initial kinetic energy is:
Initial kinetic energy = (1/2) * 0.2 kg * (velocity)^2
Since the arrow is fired from rest, the initial velocity is 0 m/s.
Initial kinetic energy = (1/2) * 0.2 kg * (0 m/s)^2
= 0 J
Since the initial kinetic energy is 0 J, all the initial energy is converted into potential energy at the highest point.
Potential energy = mass * gravity * height
where gravity is approximately 9.8 m/s^2.
Therefore, we can solve for the height of the arrow:
Potential energy = mass * gravity * height
= 0.2 kg * 9.8 m/s^2 * height
= 0 J (since the initial kinetic energy is 0 J)
Therefore, the height that the arrow goes is 0 meters.
To find the energy stored in Robin Hood's bow, we can use the formula for potential energy:
Potential Energy = Force × Distance
Given that Robin Hood exerted an average force of 100 N and pulled the bow back by 0.5 m, we can calculate the potential energy:
Potential Energy = 100 N × 0.5 m = 50 Joules
Therefore, the energy stored in Robin Hood's bow is 50 Joules.
To determine how high the arrow went, we can use the principle of conservation of energy. When the arrow is fired, the potential energy stored in the bow is converted into the kinetic energy of the arrow. At the highest point of its trajectory, all of the arrow's initial kinetic energy is converted back into potential energy.
The formula for potential energy is:
Potential Energy = mass × gravity × height
Where:
- mass is the mass of the arrow (0.2 kg)
- gravity is the acceleration due to gravity (9.8 m/s^2)
- height is the maximum height the arrow reaches.
Since the potential energy at the highest point is equal to the energy stored in the bow, we can set up the equation:
Potential Energy = mass × gravity × height
50 J = 0.2 kg × 9.8 m/s^2 × height
We can rearrange the equation to solve for the height:
height = 50 J / (0.2 kg × 9.8 m/s^2)
height ≈ 25.51 meters
Therefore, the arrow reached a height of approximately 25.51 meters.