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?
Well, if we're talking about static friction here, it's like giving your blocks a good ol' hug. So, to find the magnitude of the minimum force of static friction required, we need to calculate the total weight of both blocks that our hero, the static friction force, needs to counteract.
Let's do some math! The weight of the block on the table is 170 N, and the weight of the suspended mass is 52 N. In order to hold them both at rest, the static friction force needs to balance out this combined weight.
So, the minimum force of static friction required would be the sum of these weights: 170 N + 52 N = 222 N.
That's the amount of force our static friction hero needs to summon to keep everything from sliding away. Go, static friction force, go!
To find the minimum force of static friction required to hold both blocks at rest, we need to consider the weight of the block on the table and the weight of the suspended mass.
Let's break down the problem step-by-step:
1. Calculate the normal force for the block on the table.
- The normal force is equal to the weight of the block on the table since the block is not accelerating vertically.
- Given that the weight of the block on the table is 170 N, the normal force would also be 170 N.
2. Determine the force of gravity acting on the suspended mass.
- The weight of the suspended mass is given as 52 N.
3. Add the weight of the suspended mass to the normal force.
- Summing the weight of the suspended mass (52 N) with the normal force (170 N) gives us a total force of (52 N + 170 N) = 222 N.
4. Understand the role of static friction.
- Static friction is the force that opposes the tendency of the two surfaces to slide past each other when they are not moving relative to each other.
- The maximum force of static friction can be calculated using the equation:
F_static_friction = μ_s * N
where μ_s is the coefficient of static friction and N is the normal force.
5. Calculate the minimum force of static friction required to hold both blocks at rest.
- Since the blocks are at rest, the minimum force of static friction must be equal to the total force of (52 N + 170 N) = 222 N.
- Therefore, the magnitude of the minimum force of static friction required to hold both blocks at rest is 222 N.
Note: The coefficient of static friction is not provided in the question, so we cannot calculate the exact value of static friction. The value of static friction will depend on the coefficient of static friction between the two surfaces in contact.
To find the minimum force of static friction required to hold both blocks at rest, we need to analyze the forces acting on the system.
First, let's draw a free-body diagram for the system:
```
^
<---- Suspended Mass (52 N)
| |
| | ============
| | Table
| |
-----
Block (170 N)
```
Now, let's break down the forces acting on each block:
1. Suspended Mass (52 N):
- Weight (downward): 52 N
- Tension force (upward): This is the force acting on the suspended mass due to the string or rope. Since we are assuming the system is at rest, the tension force is equal in magnitude but opposite in direction to the weight: 52 N.
2. Block (170 N):
- Normal force (upward): This is the force exerted by the table on the block to support its weight. Since the block is at rest on the table, the normal force equals the weight of the block: 170 N.
- Force of static friction (opposite to motion): This is the force that prevents the block from sliding on the table. The direction of the force of static friction is opposite to the direction of impending or actual motion. In this case, the block is not sliding, so the force of static friction is acting in the opposite direction to the impending motion, which is zero. We can assume there is no horizontal force acting on the block.
Now, to find the minimum force of static friction required to hold both blocks at rest, we need to consider the horizontal equilibrium of forces on the block:
Sum of horizontal forces = 0
The horizontal forces acting on the block are the force of static friction and the tension force. Since there is no horizontal acceleration, the sum of these forces must be zero.
Force of static friction - Tension force = 0
Since we know the tension force is 52 N, the force of static friction must also be 52 N.
Therefore, the magnitude of the minimum force of static friction required to hold both blocks at rest is 52 N.