A string is tied to a 4.4 kg block and a 120 g hanging bucket. students add 20 g washers one at a time to the bucket. the students are unaware that the coefficient of static friction for the block on the table is 0.42. What is the maximum force of static friction for the block? how many washers can the students add to the bucket without moving the block?
Well, well, well, looks like we have some budding engineers here! Let's get down to business and solve this conundrum!
The maximum force of static friction can be found using the formula: F_max = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force.
But before we proceed, let me just clarify something: what kind of washers are these? Because if they're a bunch of slippery, soapy washers, they might just slide right off the bucket and make a mess! But, I digress...
To calculate the maximum force of static friction for the block, we need to determine the normal force acting on it. The normal force is equal to the weight of the block (mg), where m is the mass (4.4 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
So, the normal force is N = 4.4 kg * 9.8 m/s^2 = 43.12 N. That's quite a weight!
Now, let's calculate the maximum force of static friction: F_max = 0.42 * 43.12 N = 18.1056 N. That's the maximum force the block can resist without budging!
Now, how many washers can those students add without making the block move? Well, the weight of each washer is 20 g, which is equivalent to 0.02 kg. Every time a washer is added, the weight hanging on the string (and acting on the bucket) increases.
To make the block start sliding, the force of static friction needs to be exceeded. So, the sum of the weights of the bucket and the washers (acting downward) needs to exceed the maximum force of static friction (acting upward).
The weight of the bucket is 120 g, which is equivalent to 0.12 kg. Thus, the total weight hanging on the string is 0.12 kg + (0.02 kg * number of washers).
To find the maximum number of washers, we solve the inequality:
F_max < (0.12 kg + 0.02 kg * number of washers) * g
18.1056 N < (0.12 kg + 0.02 kg * number of washers) * 9.8 m/s^2
Dividing both sides by 9.8 m/s^2, we get:
1.8473 < 0.12 kg + 0.02 kg * number of washers
Subtracting 0.12 kg from both sides, we get:
1.7273 < 0.02 kg * number of washers
Dividing both sides by 0.02 kg, we finally get:
86.36 < number of washers
Hold on! I don't think that's right. 86 washers? That's a whole bucket load! Those students must have some serious ammunition!
So, there you have it! The maximum force of static friction for the block is approximately 18.1056 N, and the students can add up to 86 washers before the block starts sliding. I hope this helps, and remember, physics can be quite a slippery subject, just like those soapy washers! Good luck, my engineering friends!
To find the maximum force of static friction for the block, we can use the equation:
Force of static friction (fs) = coefficient of static friction (μ) * Normal force (N)
The normal force (N) is equal to the weight of the block.
Weight of the block = mass * gravitational acceleration
Weight of the block = 4.4 kg * 9.8 m/s^2
Next, we can calculate the weight of the hanging bucket:
Weight of the bucket = mass * gravitational acceleration
Weight of the bucket = 0.120 kg * 9.8 m/s^2
Now, we can find the total normal force acting on the block:
Total normal force (N) = weight of the block + weight of the bucket
Now, substituting the values into our equation for force of static friction, we have:
fs = 0.42 * (weight of the block + weight of the bucket)
To find the maximum force of static friction, we substitute the values:
fs = 0.42 * (4.4 kg * 9.8 m/s^2 + 0.120 kg * 9.8 m/s^2)
Now, we can calculate the force of static friction.
Next, to find the number of washers that can be added to the bucket without moving the block, we need to consider the force of static friction and the additional weight added.
The maximum force of static friction must be greater than or equal to the force exerted by the additional weight added.
Each washer has a mass of 20 g, which is equal to 0.020 kg. Therefore, the additional weight added with each washer is 0.020 kg * 9.8 m/s^2.
The number of washers that can be added is calculated by dividing the maximum force of static friction by the force exerted by each additional weight:
Number of washers = (maximum force of static friction) / (force exerted by each additional weight)
Let's calculate the maximum force of static friction and the number of washers that can be added.
To find the maximum force of static friction for the block, we need to use the equation:
\( f_{\text{static}} = \mu \cdot N \)
Where:
- \( f_{\text{static}} \) is the maximum force of static friction
- \( \mu \) is the coefficient of static friction
- \( N \) is the normal force
To find the normal force, we need to consider the forces acting on the block. In this case, there are two forces: the weight of the block and the tension force in the string.
\( N = \text{Weight} + \text{Tension} \)
The weight can be calculated as:
\( \text{Weight} = \text{mass} \cdot g \)
Where:
- mass is the mass of the block (4.4 kg)
- g is the acceleration due to gravity (9.8 m/s²)
The tension force in the string can be found by considering the forces acting on the hanging bucket. The tension force will be equal to the weight of the bucket and the added washers.
Now let's calculate the maximum force of static friction and the number of washers the students can add without moving the block:
1. Calculate the weight of the block:
\( \text{Weight} = \text{mass} \cdot g \)
\( \text{Weight} = 4.4 \, \text{kg} \times 9.8 \, \text{m/s}^2 \)
2. Calculate the tension force in the string:
\( \text{Tension} = \text{Weight of bucket} + \text{Total weight of washers} \)
\( \text{Weight of bucket} = \text{mass of bucket} \cdot g \)
\( \text{Total weight of washers} = \text{mass of each washer} \times \text{number of washers} \)
3. Calculate the normal force:
\( N = \text{Weight} + \text{Tension} \)
4. Calculate the maximum force of static friction:
\( f_{\text{static}} = \mu \cdot N \)
5. Determine the number of washers the students can add without moving the block:
\( \text{Number of washers} = \frac{{f_{\text{static}}}}{{\text{mass of each washer}}} \)
Note: Since the coefficient of static friction remains constant, the maximum number of washers the students can add without moving the block will be the same as the number of washers calculated in step 5.
A)
Normal Force = (mass)(9.81)
Fs = (coefficient of static friction (normal force)
Fs = (0.42)(43.2)
Fs = 18.1 N