A 2.30 kg block is initially at rest on a horizontal surface. A horizontal force ModifyingAbove Upper F With right-arrow of magnitude 4.92 N and a vertical force ModifyingAbove Upper P With right-arrow are then applied to the block (see the figure). The coefficients of friction for the block and surface are μs = 0.4 and μk = 0.25. Determine the magnitude of the frictional force acting on the block if the magnitude of ModifyingAbove Upper P With right-arrow is (a)9.00 N and (b)13.0 N. (The upward pull is insufficient to move the block vertically.)
To determine the magnitude of the frictional force acting on the block, we first need to analyze the forces acting on the block.
Given:
Mass of the block (m) = 2.30 kg
Horizontal force (F) = 4.92 N
Coefficient of static friction (μs) = 0.4
Coefficient of kinetic friction (μk) = 0.25
(a) When the magnitude of the vertical force (P) is 9.00 N:
The force diagram for the block looks like this:
---------------------
F --->
|
|
P --->
|
|
Frictional force (f) --->
|N| -------------------
In this scenario, the block is not moving vertically, so the magnitude of the frictional force acting on the block will be equal to the vertical force applied (P) because it has to balance the upward pull.
Therefore, the magnitude of the frictional force is 9.00 N.
(b) When the magnitude of the vertical force (P) is 13.0 N:
The force diagram for the block looks like this:
---------------------
F --->
|
|
P --->
|
|
Frictional force (f) --->
|N| -------------------
Similar to the previous case, the block is not moving vertically. Therefore, the magnitude of the frictional force acting on the block will be equal to the vertical force applied (P).
Therefore, the magnitude of the frictional force is 13.0 N.