In the situation shown in the figure, a person is pulling with a constant, nonze
ID: 2144513 • Letter: I
Question
In the situation shown in the figure, a person is pulling with a constant, nonzero force F? on string 1, which is attached to block A. Block A is also attached to block B via string 2, as shown.
For this problem, assume that neither string stretches and that friction is negligible. Both blocks have finite (nonzero) mass.
Question 1.
Which one of the following statements correctly descibes the relationship between the accelerations of blocks A and B?
A. Block A has a larger acceleration than block B.
B. Block B has a larger acceleration than block A.
C. Both blocks have the same acceleration.
D. More information is needed to determine the relationship between the accelerations.
Question 2.
How does the magnitude of the tension in string 1, T1, compare with the tension in string 2, T2?
A. T1>T2
B. T1=T2
C. T1<T2
D. More information is needed.
Explanation / Answer
Think about it this way:
When you pull on the string will the blocks move at the same time? Whichever block moves first has the higher acceleration. From the diagram and because the strings won't stretch, the blocks will move at the same time so the acceleration is the same.
Because we are essentially pulling both blocks with the force F, using Newton's 3rd law we get: F = (mass A + mass B) *a.
Since tension in a string is the same throughout the whole string, the tension in string 1, T1 has to equal F. But string 2 is only pulling mass B. That means that the tension in string 2:T2 = (mass B) *a. By substituting the two equations we get:
T1 = (mass A + mass B)*a
T2 = (mass B)*a
since we already determined that the acceleration a is the same we can easily tell that T1 is always bigger then T2.