A physical pendulum consists of a vertical board of of mass 6.12 kg, length 191 cm, and width 12 cm hanging from a horizontal, frictionless axle. A bullet of mass 143 g and a purely horizontal speed v impacts the pendulum at the bottom edge of the board. The board then makes a complete circle.

(a) If the bullet passed through the board, reducing its speed by a factor of 1/3, what is the minimum speed of the bullet?
(b) If the bullet embedded itself in the board, what is the minimum speed of the bullet?

Note (hint from instructor): It appears you may use Conservation of Energy to find angular speed. For potential energy: use center of mass. For kinetic energy, use impulse. Then, to find initial speed, use conservation of angular momentum.

Answer

A. 229.192m/s

B 158.6m/s

Explanation:

See attached file

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s

the best answer for these questions would be:

1.            c. is smaller

2.            d) concrete operational

3.            b) interaction with the environment – the children interact with their environment can them learn more.

4.            a) parents who reason openly with children can limit a child’s cognitive ability.