A Force,F=10N,applied at an angle of 37 degree above the horizontal,moves a crate a distance of 5m along a rough horizontal surface.A frictional force of 5N opposes the motion.what is the change in kinetic energy?
net force= 10*cos37-5
That is the net force, operating on a deistance of 5 meters. So that is the change in KE. netforce*distance
To find the change in kinetic energy, we need to calculate the work done.
The work done is given by the formula:
Work = Force × Distance × cos(θ)
Where:
Force = 10 N (applied force)
Distance = 5 m (distance moved)
θ = 37 degrees (angle above the horizontal)
First, we need to calculate the work done by the applied force:
Work_applied = Force × Distance × cos(θ)
= 10 N × 5 m × cos(37°)
To calculate the cosine of an angle, we can use a scientific calculator or an online calculator. The cosine of 37 degrees is approximately 0.7986.
Work_applied ≈ 10 N × 5 m × 0.7986
Next, let's calculate the work done by the frictional force:
Work_friction = Force_friction × Distance
Given that the frictional force is 5 N and the distance is 5 m, we can calculate:
Work_friction = 5 N × 5 m
Now, we can calculate the net work done:
Net Work = Work_applied - Work_friction
Substituting the values we calculated earlier:
Net Work ≈ (10 N × 5 m × 0.7986) - (5 N × 5 m)
Finally, we can find the change in kinetic energy using the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy:
Change in Kinetic Energy = Net Work
Substituting the value of the net work we calculated:
Change in Kinetic Energy ≈ (10 N × 5 m × 0.7986) - (5 N × 5 m)
By evaluating this expression, we can find the numerical value of the change in kinetic energy.