Question

How much force needs to be applied when 800J of work causes a resting 40kg Block to slide 4m over a Frictionless surface? What will the Velocity be at the end of 4m?

Answer 1

v = 6.32 [m/s]

Step-by-step explanation:

We know that work in physics is defined as the product of force by distance, in this way we have:

`W=F*d`

where:

F = force [N]

W = work [J]

d = distance = 4 [m]

`800=F*4\\F=200[N]`

Now we know that by means of Newton's second law which tells us that the total force on a body is equal to the product of mass by acceleration, we can determine the acceleration that occurs.

`F=m*a`

where:

F = force = 200 [N]

m = mass = 40 [kg]

a = acceleration [m/s²]

`a=F/m\\a=200/40\\a=5[m/s^(2) ]`

Now using this equation of kinematics we can determine the final velocity.

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

where:

vf = final velocity [m/s]

vo = initial velocity = 0 (initially at rest)

a = acceleration = 5 [m/s]

x = distance = 4 [m]

`v_(f)^(2)=0+(2*5*4)\\v_(f)=√(40)\\v_(f)=6.32[m/s]`