Question

A 6 kilogram block in outer space is moving at -100 m/s (to the left). It suddenly experiences three forces as shown below (in the attachment). What is the block’s displacement when it finally comes to rest?

Answer 1

x = 1474.9 [m]

Step-by-step explanation:

To solve this problem we must use Newton's second law, which tells us that the sum of forces must be equal to the product of mass by acceleration.

We must understand that when forces are applied on the body, they tend to slow the body down to stop it.

So as the body continues to move to the left, it is slowing down. Therefore we must calculate this deceleration value using Newton's second law. We must perform a sum of forces on the x-axis equal to the product of mass by acceleration. With leftward movement as negative and rightward forces as positive.

ΣF = m*a

`10 +12*sin(60)= - 6*a\\a = - 3.39[m/s^(2)]`

Now using the following equation of kinematics, we can calculate the distance of the block, before stopping completely. The initial speed must be 100 [m/s].

`v_(f)^(2) =v_(o)^(2)-2*a*x`

where:

Vf = final velocity = 0 (the block stops)

Vo = initial velocity = 100 [m/s]

a = - 3.39 [m/s²]

x = displacement [m]

`0 = 100^(2)-2*3.39*x\\x=(10000)/(2*3.39)\\x=1474.9[m]`