A weight of 150 lbs is placed on a smooth plane inclined at an angle of 24° with the horizontal. What is the required force needed to prevent the weight from sliding down the plane?
Fp = 150*sin24 = 61 Lbs. = Force parallel to the incline = Force required
To determine the force required to prevent the weight from sliding down the plane, we need to analyze the forces acting on the weight and consider the equilibrium condition.
First, let's decompose the weight into its components. We have the weight acting vertically downward (W) and its components parallel (W_parallel) and perpendicular (W_perpendicular) to the inclined plane.
The weight component parallel to the plane (W_parallel) can be calculated using the formula:
W_parallel = W * sin(θ)
Where:
W is the weight (150 lbs)
θ is the angle of inclination (24°)
Substituting the given values into the formula:
W_parallel = 150 lbs * sin(24°)
Next, let's look at the forces acting on the weight. There are two forces to consider: the force of gravity (W) acting vertically downward and the required force (F) acting perpendicular to the plane. The normal force (N) and the force of friction (F_friction) also act on the weight.
In equilibrium, the sum of the forces in the horizontal direction (parallel to the plane) and the sum of forces in the vertical direction (perpendicular to the plane) should be zero.
For the forces acting in the vertical direction:
Sum of forces in the vertical direction = N - W_perpendicular = 0
Since the weight perpendicular to the plane (W_perpendicular) is equal to the normal force (N), we have:
N = W_perpendicular = W * cos(θ)
Substituting the given values:
N = 150 lbs * cos(24°)
Now, let's consider the forces acting in the horizontal direction:
Sum of forces in the horizontal direction = F - F_friction - W_parallel = 0
Since the weight parallel to the plane (W_parallel) and the force of friction (F_friction) are both acting in the opposite direction to the required force (F), we have:
F - W_parallel - F_friction = 0
From this equation, we can see that the required force (F) is equal to the sum of the weight parallel to the plane (W_parallel) and the force of friction (F_friction):
F = W_parallel + F_friction
However, in this case, since the plane is said to be smooth (meaning there is no coefficient of friction), we can conclude that the force of friction (F_friction) is zero:
F = W_parallel
Substituting the calculated value for the weight parallel to the plane:
F = 150 lbs * sin(24°)
After evaluating this equation, you can calculate the required force (F) to prevent the weight from sliding down the plane.