A block with a weight of 36 N is placed on a sheet of aluminum with an inclination of 18°. The coefficients of static and kinetic friction between the block and aluminum are 0.35 and 0.23, respectively. Will the block slide down the plane?
(1 point)
Responses
No. The downward force along the plane is 3.9 N and the maximum static friction force is 34 N.
No. The downward force along the plane is 3.9 N and the maximum static friction force is 34 N.
Yes. The downward force along the plane is 34 N and the maximum static friction force is 2.6 N.
Yes. The downward force along the plane is 34 N and the maximum static friction force is 2.6 N.
Yes. The downward force along the plane is 11 N and the maximum static friction force is 7.9 N.
Yes. The downward force along the plane is 11 N and the maximum static friction force is 7.9 N.
No. The downward force along the plane is 11 N and the maximum static friction force is 12 N.
No. The downward force along the plane is 11 N and the maximum static friction force is 12 N.
No. The downward force along the plane is 3.9 N and the maximum static friction force is 34 N.
To determine whether the block will slide down the plane, we need to compare the downward force along the plane to the maximum static friction force.
The downward force along the plane can be calculated using trigonometry. The weight of the block (36 N) can be resolved into two components: one perpendicular to the plane (36*cos(18°)) and one parallel to the plane (36*sin(18°)). The component parallel to the plane is the force that tends to make the block slide down.
Given that the coefficient of static friction between the block and aluminum is 0.35, the maximum static friction force can be found by multiplying the coefficient by the perpendicular force acting on the block (36*cos(18°)).
Now we can calculate the values and compare them:
1. Downward force along the plane = 36*sin(18°) ≈ 11 N
2. Maximum static friction force = 0.35 * (36*cos(18°)) ≈ 7.9 N
Comparing the two values, we see that the maximum static friction force (7.9 N) is greater than the downward force along the plane (11 N). This means that the static friction will be able to hold the block in place, and it will not slide down the plane.
Therefore, the correct answer is:
No. The downward force along the plane is 11 N and the maximum static friction force is 7.9 N.