Physics help please!!!!?

Question

An aluminum block is pushed to the right with an initial speed of v= 10 ft/s at the same time that a copper block is pushed to the left with an initial speed of v = 16 ft/s. Both blocks slide along a horizontal steel floor toward each other. If the blocks were initially 10 feet apart, determine how far each block slides before they collide into each other. Assume that the coefficient of kinetic friction between the aluminum block and the steel floor is 0.47 and the coefficient of kinetic friction between the copper block and the steel floor is 0.36.

Answer 1

Read your text books and consult with your peers.

I am sure you are bright enough to figure it out!

Answer 2

Working formula:

S = Vo(T) + (1/2)(a)T^2

where

Vo = initial velocity

T = time travelled before collision

a = acceleration

S = distance travelled by each block at collision

By definition,

a =coeff of friction * g

where g = acceleration due to gravity = 32.2 ft/sec^2

For the aluminum block:

Vo = 10

a = 0.47 * 32.2 = 15.134 ft/sec^2

S = distance travelled before collision

Substituting values,

S = 10T + (1/2)(-15.134)T^2

NOTE the negative sign attached to the acceleration. This simply denotes that the block is slowing down before collision due to friction.

Simplifying the above,

S = 10T - 7.567T^2  -- call this Equation A

For the copper block,

Vo = 16

a = 0.36 * 32.2 = 11.592 ft/sec^2

(10 - S) = distance travelled before collision

Substituting appropriate values,

(10 - S) = 16T + (1/2)(-11.592)T^2

Simplifying and solving for "S",

S = 10 - 16T +  5.796T^2  --  call this Equation B

Since Equation A = Equation B,

10T - 7.567T^2 = 10 - 16T +  5.796T^2

Combining like terms,

13.363T^2 - 26T + 10 = 0

Using the quadratic formula to solve for "T",

T = 0.53 and T = 1.42

The second root will be ignored. We will just consider T = 0.53 as the time the two blocks have travelled before colliding.

Since the value of "T" has been determined,then from Equation A,

S = 10(.53) - 7.567(.53)^2

S = 3.17

ANSWER:

Before collision, the aluminum block has travelled 3.17 feet while the copper block has travelled 6.83 feet (10 - 3.17 = 6.83).

Hope this helps.