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 moving with a constant speed, the net force on them is zero. Therefore, the upward force from the tension in the wire must be equal and opposite to the downward force of gravity on the weights. The weight of each object is given by:

w = mg

where m is the mass of the object and g is the acceleration due to gravity (9.81 m/s²). Since the objects have equal masses, their weights are equal:

w = m1g + m2g = 5 kg × 9.81 m/s² = 49.05 N

The tension in the wire is given by:

T = P - w

Therefore,

P = T + w

We can see that choice D is the only one that matches this relationship. Therefore, the correct answer is D.

Two Weights Are Connected by a Massless Wire and Pulled