1. The weight in the following diagram has a mass of 0.750 kg and the cart has a mass of 0.52 kg. There is a friction force of 2.1 N acting on the cart. What is the tension in the string?
a. 4.4 N
b. 4.3 N
c. 4.1 N
d. 4.2 N
2. An 8.5 kg block is attached to a weight. The coefficient of static friction between the block and the table is 0.71. What is the minimum mass required for the weight in order to start the block in motion?
a. 6.0 kg
b. 7.0 kg
c. 4.0 kg
d. 5.0 kg
For both problems, there is a diagram with a pulley between the weight and the block/cart
For #1 I got 4.04N, but that isn't an option. I used f=ma where f=2.1N and m=0.52kg
For #2 i think the answer is A.
See
http://www.jiskha.com/display.cgi?id=1496429854
Please show your attempt for part 2.
You need to draw separate FBD (free body diagrams) for the block and weight. Also, please describe the diagram in words, i.e. confirm whether the weight is free-hanging.
1. To find the tension in the string, we can consider the forces acting on the system.
The weight has a mass of 0.750 kg, so its weight (W) can be calculated as W = mg, where g is the acceleration due to gravity (9.8 m/s^2). Thus, W = 0.750 kg * 9.8 m/s^2 = 7.35 N.
Since the weight is connected to the cart by a string, the tension in the string (T) is equal to the weight. Therefore, T = 7.35 N.
None of the given options (a, b, c, d) match the calculated tension. It's possible that there may be an error in the provided options, or additional information is needed to solve the problem correctly.
2. To determine the minimum mass required for the weight to start the block in motion, we can consider the static friction between the block and the table.
The maximum static friction force (F_s_max) can be calculated using the equation F_s_max = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force on the block.
The normal force (N) is equal to the weight of the block (mg), where g is the acceleration due to gravity (9.8 m/s^2).
Therefore, N = 8.5 kg * 9.8 m/s^2 = 83.3 N.
Substituting the given coefficient of static friction (μ_s = 0.71) and the calculated normal force (N = 83.3 N) into the equation F_s_max = μ_s * N, we can find F_s_max.
F_s_max = 0.71 * 83.3 N = 59.143 N.
To overcome the static friction and set the block in motion, the weight must exert a force equal to or greater than the maximum static friction force (F_s_max).
Therefore, the minimum mass required for the weight is 59.143 N divided by the acceleration due to gravity (g = 9.8 m/s^2):
Minimum mass = F_s_max / g = 59.143 N / 9.8 m/s^2 ≈ 6.03 kg.
The closest option to the calculated minimum mass is option A, which is 6.0 kg.
To answer both questions correctly, let's break down the steps to find the solutions.
1. Calculating the tension in the string:
To determine the tension in the string, you can use Newton's second law, where force (F) equals mass (m) multiplied by acceleration (a). In this case, the force is the tension in the string (T), the mass is the weight (0.750 kg), and the acceleration is the friction force (2.1 N).
T = m * a
T = 0.750 kg * 2.1 N
T ≈ 1.575 N
Therefore, the tension in the string is approximately 1.575 N. Since none of the provided answer options match exactly, it seems there might be a calculation error in the given options.
2. Finding the minimum mass required for the weight:
To find the minimum mass required for the weight to start the block in motion, we need to consider the force of static friction (fs) acting between the block and the table. The force of static friction can be given by the coefficient of static friction (μs) multiplied by the normal force (N). The normal force for an object on a horizontal surface is equal to its weight (mg).
fs ≤ μs * N
fs ≤ μs * mg
In this case, the force of static friction (fs) can be represented by the tension in the string (T) because it opposes the motion of the block. The coefficient of static friction (μs) is provided as 0.71, and the mass of the block (m) is 8.5 kg.
T ≤ μs * mg
T ≤ 0.71 * 8.5 kg * g
To find the minimum mass required for the weight, we need to find the mass value where the tension in the string is equal to the maximum force of static friction (fs).
For option A (6.0 kg):
T = 0.71 * 6.0 kg * g
T = 4.26 kg * g
But this value is not equal to T, so option A is not the correct answer.
By testing the remaining options, we can find the minimum mass required for the weight:
T = 0.71 * 7.0 kg * g
T = 4.97 kg * g
Since T is less than 4.97 kg * g for option B, it is also not the correct answer.
T = 0.71 * 4.0 kg * g
T = 2.84 kg * g
In this case, T is greater than 2.84 kg * g for option C. Thus, the minimum mass required for the weight is approximately 4.0 kg.
Therefore, the correct answer for question 2 is option C (4.0 kg).