a simple pendulum of length 0.2m has bob of mass 5gm, it is pulled aside through an angle 60 degrees from the vertical. a spherical body of mass 2.5gm is placed at the lowest position of the bob. when the bob is released it strikes the spherical body and comes to rest.what is the velocity of the spherical body?(g=9.8 m/s)
Whare is the solution
2.8
To find the velocity of the spherical body when the pendulum strikes it, we can use the principle of conservation of mechanical energy. The initial potential energy of the pendulum bob is converted into the kinetic energy of the spherical body.
First, let's calculate the potential energy of the pendulum bob at the highest point. The potential energy is given by the formula P.E. = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
Given:
- Mass of the pendulum bob (m1) = 5 g = 0.005 kg
- Length of the pendulum (L) = 0.2 m
- Angle from the vertical (θ) = 60 degrees
To find the height (h), we can use trigonometry. The height (h) is given by the equation h = L(1 - cosθ).
So, h = 0.2(1 - cos60°) = 0.2(1 - 0.5) = 0.1 m
Now, calculate the potential energy (P.E.) of the pendulum bob:
P.E. = mgh = 0.005 × 9.8 × 0.1 = 0.0049 J
Since the pendulum comes to rest, all of its potential energy is converted into the kinetic energy of the spherical body after the collision.
The kinetic energy (K.E.) of the spherical body can be calculated using the formula K.E. = 0.5mv^2, where m is the mass and v is the velocity.
Given:
- Mass of the spherical body (m2) = 2.5 g = 0.0025 kg
Using the principle of conservation of energy, we equate the potential energy of the pendulum bob to the kinetic energy of the spherical body:
0.0049 J = 0.5 × 0.0025 × v^2
Simplifying the equation, we get:
v^2 = (2 × 0.0049) / 0.0025
v^2 = 0.0196 / 0.0025
v^2 = 7.84
v = sqrt(7.84)
v ≈ 2.8 m/s
Therefore, the velocity of the spherical body when the pendulum strikes it is approximately 2.8 m/s.
Again, what does conservation of energy mean? You have to do a little figuring here, how high is the pendulum initially.
Are you answer grazing?