A 17.9 kg block is dragged over a rough, hor- izontal surface by a constant force of 74.1 N acting at an angle of angle 32.3◦ above the horizontal. The block is displaced 72.4 m and the coefficient of kinetic friction is 0.242. Find the work done by the 74.1 N force. The acceleration is 9.8 m/s^2. Ansewer in units of J.
Work = Fap*cosA * d=74.1*cos32.3 * 72.4
= 4535 J.
To find the work done by the 74.1 N force, we need to calculate the net force acting on the block and then multiply it by the displacement.
1. Let's start by finding the vertical component of the force. We can use trigonometry to do this:
F_vertical = F * sin(theta) = 74.1 N * sin(32.3°)
2. Next, we can find the frictional force acting on the block:
F_friction = μ * N, where N is the normal force
N = m * g, where m is the mass of the block and g is the acceleration due to gravity
F_friction = μ * m * g = 0.242 * 17.9 kg * 9.8 m/s^2
3. Now, we can find the horizontal component of the force:
F_horizontal = F * cos(theta) = 74.1 N * cos(32.3°)
4. The net force acting on the block in the horizontal direction is given by:
F_net = F_horizontal - F_friction
5. Finally, we can calculate the work done:
Work = F_net * d, where d is the displacement of the block
Work = (F_horizontal - F_friction) * d = (F * cos(theta) - μ * m * g) * d
Now we can substitute the given values into the equation above to find the work done.
To find the work done by the 74.1 N force, we can break it down into two components: the force acting parallel to the displacement (the horizontal force) and the force acting perpendicular to the displacement (the vertical force).
Given:
- Mass of the block (m) = 17.9 kg
- Applied force (F) = 74.1 N
- Angle above the horizontal (θ) = 32.3°
- Displacement (d) = 72.4 m
- Coefficient of kinetic friction (μ) = 0.242
- Acceleration due to gravity (g) = 9.8 m/s^2
First, let's calculate the horizontal force component:
F_horizontal = F * cos(θ)
F_horizontal = 74.1 N * cos(32.3°)
F_horizontal = 63.16 N
Next, we need to calculate the work done against friction. The work done against friction can be determined using the equation:
Work_friction = force_friction * displacement
To find the force of friction, we use the equation:
force_friction = friction coefficient * normal force
To obtain the normal force, we use the equation:
normal force = mass * acceleration due to gravity
normal force = 17.9 kg * 9.8 m/s^2
normal force = 175.22 N
Now we can calculate the force of friction:
force_friction = 0.242 * 175.22 N
force_friction = 42.37 N
Finally, we can calculate the work done against friction:
Work_friction = force_friction * displacement
Work_friction = 42.37 N * 72.4 m
Work_friction = 3069.388 J (to three decimal places)
Since the applied force is at an angle of 32.3° above the horizontal, it does work in both the horizontal and vertical directions. However, since the vertical component of the force doesn't contribute to the horizontal displacement, we only need to consider the horizontal component.
Therefore, the work done by the 74.1 N force is equal to the work done against friction:
Work = Work_friction
Work = 3069.388 J
Hence, the work done by the 74.1 N force is 3069.388 J.