A simple pendulum of length 1m has a wooden bob of mass 1kg.it is strike by a bullet of mass 10^-20 kg moving with a speed of 2×10^2m/s.The bullet gets embedded into the bob. Obtain the height to which the bob rest before swing back.
To find the height to which the bob rises before swinging back, we can use the principle of conservation of energy.
The initial energy of the system is the kinetic energy of the bullet just before impact. The final energy of the system is the potential energy of the bob at the highest point of its swing, when it momentarily stops moving and reaches its maximum elevation.
First, let's find the initial kinetic energy of the bullet:
Initial kinetic energy (KE) = 1/2 * mass bullet * (velocity bullet)^2
= 1/2 * (10^-20 kg) * (2 × 10^2 m/s)^2
Next, let's find the height to which the bob rises. At the highest point of its swing, all its initial kinetic energy is converted into potential energy:
Potential energy (PE) = mass bob * gravity * height bob
Since the bullet gets embedded in the bob, the mass of the system after impact is the mass of the bob plus the mass of the bullet:
Final mass (mass bob + mass bullet) = 1 kg + 10^-20 kg
Now, equating the initial kinetic energy to the final potential energy, we have:
1/2 * (10^-20 kg) * (2 × 10^2 m/s)^2 = (mass bob + mass bullet) * gravity * height bob
Substituting the values we have:
1/2 * (10^-20 kg) * (2 × 10^2 m/s)^2 = (1 kg + 10^-20 kg) * 9.8 m/s^2 * height bob
Simplifying, we obtain:
10^-22 J = (1 kg + 10^-20 kg) * 9.8 m/s^2 * height bob
To find the height bob, we rearrange the equation:
height bob = 10^-22 J / [(1 kg + 10^-20 kg) * 9.8 m/s^2]
Calculating this value, we get:
height bob ≈ 5.10 × 10^-23 meters
Therefore, the bob rises to a height of approximately 5.10 × 10^-23 meters before swinging back.
momentum is conserved ... find the velocity of the bullet/bob after impact
calculate the kinetic energy of the bullet/bob
the K.E. becomes P.E. ... 1/2 m v^2 = m g h ... h = v^2 / (2 g)