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?
Here's a hint:
(Work done by Juana) - (Work done against friction)
= (Increase in kinetic energy)
Use the final kinetic energy to get the speed.
The friction force is
Ff = M*g*(0.12) = 66.8 N
The work done against friction is
Ff*1.3 = 209.6 J
The work done pulling is 124N*1.3m = 161.2 J
The difference becomes kinetic energy
1.3
To find the final speed of the crate, we can use the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy.
The work done on the crate is given as 74.4 J. The change in kinetic energy is equal to the final kinetic energy minus the initial kinetic energy. Since the crate starts at rest, the initial kinetic energy is zero.
So, the work done on the crate is equal to the final kinetic energy:
Work = Change in kinetic energy
74.4 J = (1/2) * m * v^2
Where:
m = mass of the crate = 56.8 kg
v = final velocity of the crate
To find the final velocity, we need to rearrange the equation:
v^2 = (2 * Work) / m
v^2 = (2 * 74.4 J) / 56.8 kg
Now, we can calculate the value of v:
v^2 = 2.6056 J/kg
v ≈ √(2.6056) m/s
v ≈ 1.6141 m/s
Therefore, the final speed of the crate is approximately 1.6141 m/s.
To find the final speed of the crate, we can use the work-energy theorem. The work done on an object is equal to the change in its kinetic energy. In this case, the work done on the crate is 74.4 J.
The work done on an object is calculated using the formula:
Work = Force x Distance x cos(theta)
Where:
- Force is the applied force on the object (124 N)
- Distance is the displacement of the object (1.3 m)
- cos(theta) is the angle between the applied force and the direction of displacement (since the force is horizontal, cos(theta) = 1)
Therefore, 74.4 J = 124 N x 1.3 m x cos(0)
Next, we need to calculate the frictional force experienced by the crate. The frictional force can be determined using the equation:
Frictional Force = Coefficient of Kinetic Friction x Normal Force
The normal force is equal to the weight of the crate, which can be calculated as:
Normal Force = mass x gravity
Where:
- mass of the crate is 56.8 kg
- gravity is approximately 9.8 m/s^2
So, Normal Force = 56.8 kg x 9.8 m/s^2
Once we have the frictional force, we can calculate the work done against friction, which is equal to the force of friction multiplied by the displacement:
Work against Friction = Frictional Force x Distance
Now, we can determine the net work done on the crate:
Net Work = Work - Work against Friction
Finally, we can equate the net work done to the change in kinetic energy:
Net Work = Change in Kinetic Energy
The initial kinetic energy is zero because the crate starts at rest. Therefore:
Change in Kinetic Energy = Final Kinetic Energy
Using the formula for kinetic energy:
Final Kinetic Energy = (1/2) x mass x velocity^2
We can solve for the final velocity by rearranging the equation:
Final velocity = sqrt((2 x Net Work) / (mass))
Now we can plug in the known values and calculate the final speed of the crate.