A 5.5 g coin sliding to the right at 21.0 cm/s makes an elastic head-on collision with a 16.5 g coin that is initially at rest. After the collision, the 5.5 g coin moves to the left at 10.5 cm/s. (a) Find the final velocity of the other coin. cm/s (b) Find the amount of kinetic energy transferred to the 16.5 g coin. J

(a) 10.33 cm/s

(b) 0.00088 J

Explanation:

Parameters given:

Mass of first coin, m = 5.5g = 0.0055kg

Mass of second coin, M = 16.5 = 0.0165kg

Initial velocity of first coin, u = 21 cm/s

Final velocity of first coin, v = -10cm/s (because it's in the opposite direction of the initial motion)

Initial velocity of second coin, U = 0 cm/s

(a) Using principle of conservation of momentum:

Total initial momentum = Total final momentum

m*u + M*U = m*v + M*V

U = 0

=> m*u + 0 = m*v + M*V

m*u - m*v = M*V

V = m(u - V) / M

V = 0.0055(21 - (-10)) / 0.0165

V = 0.3333 * 31 = 10.33 cm/s

(b) Kinetic energy is given as:

KE = 0.5 * M * V²

V = 10.33 cm/s = 0.1033 m/s

KE = 0.5 * 0.0165 * 0.1033²

KE = 0.00088 J

Explanation:

Given length is

Circumference of a circle is given as:

a.But the circumference is equal to length of the wire. Therefore circumference as a function of is:

b.Area as function of

Area is calculated as

Rewrite the circumference equation to make r the subject of the formula.

To express area as a function of :-

Therefore area of circle as a function of is