While trying to decide where to hang a framed picture, you press it against the wall to keep it from falling. The picture weighs 5.0 N and you press against the frame with a force of 6.0 N at an angle of 40 ° from the vertical. (a) What is the direction of the normal force exerted on the picture by your hand? (b) What is the direction of the normal force exerted on the picture by the wall? (c) What is the coefficient of static friction between the wall and the picture? The frictional force exerted on the picture by the wall can have two possible directions. Explain why.
a. Perpendicular to and toward the frame and wall.
b. Opposite direction of normal force exerted by hand.
c. A = 90 - 40 = 50 Deg., CCW.
Fv = 5 + 6*sin50 = 9.60 N. = Normal.
Fn = Fap - u*Fv = 0.
6*cos(50) - u*9.6 = 0.
9.6u = 6*cos(50) = 3.86.
u = 3.86 / 9.6 = 0.402.
If the picture was placed on the opposite wall, the angle would be:
A = 90 + 40 = 130 Deg.
The cosine would be negative and the
coefficdient of friction and force ot
friction would be in opposite direction.
(a) The normal force exerted on the picture by your hand is directed perpendicular to the surface of contact. In this case, your hand is pressing against the picture at an angle of 40° from the vertical. Therefore, the normal force will be directed at an angle of 40° from the horizontal.
(b) The normal force exerted on the picture by the wall is also directed perpendicular to the surface of contact. Since the picture is pressed against the wall, the wall is providing the support or the reaction force. Hence, the normal force exerted by the wall will be directed opposite to the force applied by your hand, i.e., vertically upwards.
(c) The coefficient of static friction between the wall and the picture cannot be determined based on the given information. The frictional force exerted on the picture by the wall can have two possible directions: parallel to the surface of contact and directed either upward or downward. The direction of the frictional force depends on the direction of the proposed motion or tendency of motion of the picture. If the picture tends to slide upwards, the frictional force will be pointing downwards, and if the picture tends to slide downwards, the frictional force will be pointing upwards. Without knowing the direction of the proposed motion, we cannot determine the coefficient of static friction.
To answer these questions, we need to break down the forces acting on the picture and understand the concept of normal forces.
(a) The direction of the normal force exerted on the picture by your hand can be determined using the principle that the normal force is always perpendicular to the surface it acts on. In this case, your hand is pressing against the frame of the picture at an angle of 40° from the vertical. Since the normal force is always perpendicular to the surface, it will be in the direction opposite to the angle you are pressing. Therefore, the direction of the normal force will be 40° from the vertical in the opposite direction.
(b) The direction of the normal force exerted on the picture by the wall can be determined using the same principle. Since the picture is pressed against the wall, the normal force exerted by the wall will be perpendicular to the wall surface. Thus, the direction of the normal force exerted on the picture by the wall will be perpendicular to the wall surface, pointing away from the wall.
(c) The coefficient of static friction between the wall and the picture can be calculated using the formula:
Coefficient of static friction = (Force of friction) / (Normal force)
To calculate the force of friction, we need to consider the direction of the normal force exerted by the wall. As mentioned earlier, the normal force by the wall is pointing away from the wall. Depending on the situation, the force of friction can act in either of two opposite directions (parallel or anti-parallel to the wall) to balance the forces and keep the picture in place. So, the frictional force exerted on the picture by the wall can have two possible directions.
In order to find the coefficient of static friction, we need more information, such as the magnitude of the force of friction and the normal force.