Two weights are connected by a massless wire and pulled upward with a constant speed of 1.50 m/s by a vertical pull P.The tension in the wire is T (see figure).Which one of the following relationships between T and P must be true?
A) T P
B) T = P
C) P + T = 125 N
D) P = T + 25 N
E) P = T + 100 N

Question

Two weights are connected by a massless wire and pulled upward with a constant speed of 1.50 m/s by a vertical pull P.The tension in the wire is T (see figure).Which one of the following relationships between T and P must be true? 
A) T > P 
B) T = P 
C) P + T = 125 N 
D) P = T + 25 N 
E) P = T + 100 N

Quizplus · Accepted Answer

Since the weights are pulled upward with a constant speed, the net force on them is zero. This means that the upward force P applied by the pull must be equal to the weight of the weights plus the tension in the wire, which is T. Therefore, we have:

P = T + mg

where m is the total mass of the weights and g is the acceleration due to gravity. Rearranging this equation, we get:

P - mg = T

This shows that the tension in the wire is equal to the difference between the upward force applied and the weight of the weights. Since the weights are being pulled upward, their weight opposes this motion and acts downward, so we have:

mg = 25 N

Substituting this into the previous equation, we get:

P - 25 N = T

Therefore, the relationship between T and P is:

P = T + 25 N

So, the correct answer is D.

Two Weights Are Connected by a Massless Wire and Pulled