An arrow is shot by stretching a bow through a distance of 0.9m by applying a force of 150N, the mass of the arrow is 1.7kg. Using the conservation of energy, calculate the speed with which the arrow leaves the bow.
To calculate the speed with which the arrow leaves the bow using the conservation of energy, we need to apply the principle of conservation of mechanical energy.
The initial potential energy of the arrow when it is stretched is given by the equation:
Potential Energy (PE) = Force × Distance
PE = 150N × 0.9m = 135 Joules
According to the conservation of energy, the potential energy will be converted into kinetic energy when the bow is released. The kinetic energy of the arrow is given by the equation:
Kinetic Energy (KE) = 1/2 × Mass × Velocity^2
We can rearrange this equation to find the velocity:
Velocity = sqrt((2 × KE) / Mass)
Since the initial potential energy is equal to the final kinetic energy, we can substitute the values:
Velocity = sqrt((2 × 135 J) / 1.7 kg)
Calculating this equation, we find:
Velocity = sqrt(270 / 1.7) m/s
Velocity ≈ sqrt(158.82) m/s
Velocity ≈ 12.6 m/s
Therefore, the speed with which the arrow leaves the bow is approximately 12.6 m/s.
To calculate the speed with which the arrow leaves the bow using the conservation of energy, we need to find the potential energy stored in the bow when it is stretched and then convert it into kinetic energy when the arrow is released.
1. Calculate the potential energy stored in the bow:
Potential energy (PE) = force (F) x distance (d)
PE = 150N x 0.9m
PE = 135 J
2. Convert the potential energy into kinetic energy:
Kinetic energy (KE) = potential energy (PE)
KE = 135 J
3. Apply the equation for kinetic energy:
KE = (1/2) x mass (m) x velocity^2 (v^2)
135 J = (1/2) x 1.7 kg x v^2
4. Rearrange the equation to solve for velocity:
v^2 = (2 * 135 J) / 1.7 kg
v^2 = 159.41 m^2/s^2
5. Take the square root to find the velocity:
v = √159.41 m^2/s^2
v ≈ 12.62 m/s
Therefore, the speed with which the arrow leaves the bow is approximately 12.62 m/s.