Answer:
Net work = W_applied + W_gravity + W_friction
= F_applied * (√3/2) * 3.0 m + F_gravity * 3.0 m * 0 + F_friction * 3.0 m * 0
Since the cosine of 90° is 0, the terms involving F_gravity and F_friction will be multiplied by 0, resulting in their contribution to the net work being zero. Therefore, the equation simplifies to:
Net work = F_applied * (√3/2) * 3.0 m
Now, you can substitute the values:
Net work = F_applied * (√3/2) * 3.0 m
Remember that the value of F_applied is not given in the given information. To calculate the net work, you need to know the value of F_applied.
Step-by-step explanation:
To find the work done by the force on the block, we need to consider the different forces acting on the block and calculate the net work done.
The forces acting on the block are:
1. The horizontal component of the applied force.
2. The force of gravity acting vertically downward.
3. The force of kinetic friction opposing the motion.
Let's break down the calculation step by step:
1. Calculate the horizontal component of the applied force:
The horizontal component of the applied force can be found by multiplying the magnitude of the applied force by the cosine of the angle it makes with the horizontal.
F_applied_horizontal = F_applied * cos(30°)
2. Calculate the force of gravity:
The force of gravity can be found by multiplying the mass of the block by the acceleration due to gravity.
F_gravity = m * g
where m = 2.0 kg (mass of the block) and g = 9.81 m/s² (acceleration due to gravity).
3. Calculate the force of kinetic friction:
The force of kinetic friction can be found by multiplying the coefficient of kinetic friction (µ) by the normal force (which is equal to the weight of the block).
F_friction = µ * N
where µ = 0.30 (coefficient of kinetic friction) and N = F_gravity.
4. Calculate the work done by each force:
The work done by each force can be calculated using the formula: work = force * displacement * cos(θ).
For the applied force, the displacement is along the direction of the force, so θ = 0°.
For the force of gravity and the force of kinetic friction, the displacement is perpendicular to the force, so θ = 90°.
Work done by the applied force: W_applied = F_applied_horizontal * displacement * cos(0°)
Work done by the force of gravity: W_gravity = F_gravity * displacement * cos(90°)
Work done by the force of kinetic friction: W_friction = F_friction * displacement * cos(90°)
5. Calculate the net work done:
The net work done is the sum of the work done by each force.
Net work = W_applied + W_gravity + W_friction
Now let's substitute the given values and calculate the work done by the force:
F_applied_horizontal = F_applied * cos(30°)
= F_applied * (√3/2) (cosine of 30° is √3/2)
F_gravity = m * g
= 2.0 kg * 9.81 m/s²
F_friction = µ * N
= 0.30 * F_gravity
W_applied = F_applied_horizontal * displacement * cos(0°)
= F_applied * (√3/2) * 3.0 m
W_gravity = F_gravity * displacement * cos(90°)
= F_gravity * 3.0 m * 0 (cosine of 90° is 0)
W_friction = F_friction * displacement * cos(90°)
= F_friction * 3.0 m * 0 (cosine of 90° is 0)
Net work = W_applied + W_gravity + W_friction
Calculating the values will give you the work done by the force on the block.