A force of 55 N at an angle of 32 degrees to the horizontal is applied to drag a 15kg box across a horizontal floor at a velocity of 2.5 m/s. The coefficient of friction between the box and the floor is 0.25 and the box is moved 15m across the floor. How much work is done by the force applied?
Wb = M*g = 15 * 9.8 = 147 N.
Fn = 147 - 55*sin32 = 117.9 N. = Normal force.
Fk = u*Fn = 0.25 * 117.9 = 29.5 N. = Force of kinetic friction.
Work = (55*Cos32-29.5) * 15 = 257 Joules.
To calculate the amount of work done by the applied force, you need to know the definition of work and use the formula:
Work = Force × Displacement × cos(θ),
where:
- Work is the amount of work done by the force (in joules, J)
- Force is the magnitude of the applied force (in newtons, N)
- Displacement is the distance the box is moved (in meters, m)
- θ (theta) is the angle between the applied force and the direction of displacement (in degrees)
In this case, you're given:
- Force = 55 N
- Displacement = 15 m
- θ (theta) = 32 degrees
First, convert the angle from degrees to radians:
θ (radians) = θ (degrees) × π/180
θ (radians) = 32 × π/180 ≈ 0.558 radians
Then, use the formula to calculate the work done:
Work = 55 N × 15 m × cos(0.558)
Now, let's calculate the cosine of 0.558 radians:
cos(0.558) ≈ 0.869
Substituting the values:
Work = 55 N × 15 m × 0.869
Finally, we can calculate the work done:
Work ≈ 699.42 J
Therefore, the work done by the applied force is approximately 699.42 joules.