juana slides a crate along the floor of the moving van the coefficient of kinetic friction between the crate and van floor is 0.120 the crate has a mass of 56.8 kg and juana pushes with horizontal force of 124 N. if 74.4 J of work are done on crate and the delta x is 1.3m. what is the final speed if the crate starts at rest?
To find the final speed of the crate, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
The work done on the crate is given as 74.4 J. This work is done by the external force exerted by Juana, which is 124 N. The displacement of the crate, delta x, is 1.3 m.
We can calculate the change in kinetic energy using the equation:
Work = Change in Kinetic Energy
74.4 J = (1/2) * m * v^2 - (1/2) * m * u^2
where m is the mass of the crate, v is the final velocity, and u is the initial velocity.
Since the crate starts at rest (u = 0), the equation simplifies to:
74.4 J = (1/2) * m * v^2
Now, we can substitute the given values:
74.4 J = (1/2) * 56.8 kg * v^2
To solve for v, we can rearrange the equation:
v^2 = (2 * 74.4 J) / (56.8 kg)
v^2 = 2.61 m^2/s^2
Finally, taking the square root of both sides, we find:
v ≈ 1.61 m/s
Therefore, the final speed of the crate, after Juana slides it along the floor of the moving van, is approximately 1.61 m/s.