A 170 N block rests on a table.The suspended mass has a weight of 52N.
What is the magnitude of the minimum force of static friction required to hold both blocks at rest?
What minimum coefficient of static friction is required to ensure that both blocks remain at rest?
To find the magnitude of the minimum force of static friction required to hold both blocks at rest, we need to consider the forces acting on the system.
First, let's analyze the forces acting on the 170 N block:
- Weight (W1) = 170 N (acting downward)
- Normal force (N) = 170 N (since the block is at rest on the table)
For the suspended mass:
- Weight (W2) = 52 N (acting downward)
- Tension in the rope (T) = 52 N (since the suspended mass is at rest)
Now, let's consider the forces acting horizontally:
- Force of static friction (f) = ? (acting to the right, opposing the impending motion)
For both blocks to remain at rest, the net force in the horizontal direction must be zero.
Net force (Fnet) = Force of static friction (f) - Tension in the rope (T) = 0
Since Tension (T) is equal to the weight of the hanging mass (W2), we have:
f - 52 N = 0
f = 52 N
Therefore, the magnitude of the minimum force of static friction required to hold both blocks at rest is 52 N.
To find the minimum coefficient of static friction required, we can use the equation:
f = μ * N
where μ is the coefficient of static friction and N is the normal force.
From the previous analysis, we know that N = 170 N. Substituting this value into the equation, we have:
52 N = μ * 170 N
Dividing both sides by 170 N, we get:
μ = 52 N / 170 N
μ ≈ 0.306
Therefore, the minimum coefficient of static friction required to ensure that both blocks remain at rest is approximately 0.306.
To determine the magnitude of the minimum force of static friction required to hold both blocks at rest, we need to compare the weight of the block on the table and the weight of the suspended mass.
Given:
Weight of the block on the table = 170 N
Weight of the suspended mass = 52 N
Since the block on the table is at rest, the force of static friction must balance the weight of the suspended mass. Therefore, the magnitude of the minimum force of static friction required is equal to the weight of the suspended mass:
Magnitude of the minimum force of static friction = Weight of the suspended mass = 52 N.
To determine the minimum coefficient of static friction required to ensure that both blocks remain at rest, we can use the equation:
Coefficient of static friction (μ) = Magnitude of the minimum force of static friction / Weight of the block on the table.
Plugging in the values:
Coefficient of static friction (μ) = (Magnitude of the minimum force of static friction) / (Weight of the block on the table) = 52 N / 170 N.
Coefficient of static friction (μ) = 0.3059 (approximately).
Therefore, the minimum coefficient of static friction required to ensure that both blocks remain at rest is approximately 0.3059.