A 15 kg box sits on a horizontal force.
the coefficient of static fricition between the box and the surface is 0.70. if a force P is exerted on the box at an angle directed 37 degrees below the horizontal, what must be the magnitude of P to get the box moving??
force down = 15 * 9.8 + P sin 37
force horizontal = P cos 37
0.7 (15 + P sin 37) = P cos 37
How can a box sit on a force? Do you mean that it sits on a horizontal surface?
The vertical force applied to the surface by the box is
15*g + P*sin37.
The maximum friction force (which starts it moving) is
Ff = 0.70(15*g + P*sin37)
This must equal the horizontal component of P, so
Pcos37 = 15*g + P*sin37
P(cos37 - sin37) = 15 g
P = (15/0.1968)*g = 747 N
i mean horizontal surface not horizontal force..sorry..
I believe Damon neglected to include a g term when considering the weight of the mass. Otherwise, we agree.
To find the magnitude of force P required to get the box moving, we need to consider the forces acting on the box.
Let's break down the forces acting on the box:
1. Weight (mg): The weight of the box pulling it downward can be calculated as weight = mass x acceleration due to gravity ≈ 15 kg x 9.8 m/s² = 147 N.
2. Normal force (N): The normal force is equal and opposite to the weight when the box is sitting on a horizontal surface, so N ≈ 147 N.
3. Force of friction (f): The static friction force acts in the opposite direction to the applied force and prevents the box from moving. It can be calculated as the product of the coefficient of static friction (μs) and the normal force, so f = μsN.
4. Force P: This is the force applied at an angle of 37 degrees below the horizontal.
To get the box moving, the force applied, P, must overcome the static friction force, f. Once the box starts moving, a different type of friction called kinetic friction will come into play, but for now, we will focus on static friction.
The static friction force (f) can be given by the equation: f ≤ μsN. The equality holds at the point of impending motion.
Since the box is just on the verge of moving, the force applied (P) should be equal to the maximum static friction force (f) to overcome it. Therefore, we have:
P = μsN ≤ μs(weight)
Substituting the given values, we have:
P ≤ 0.70 x 147 N
Therefore, the magnitude of force P to get the box moving must be less or equal to 102.9 N (0.70 x 147 N).