Question

Topic : Laws of Motion, FBD
Can I get the solution to this question?
Translated : Calculate the velocity of A in this image. I tried to apply 10msin37 degree = T, next?

Answer 1

Given :

Velocity of block B = 10 m/s

Mass of block B = M

Mass of block A = m

To Find :

Velocity of block A

Solution :

Just remember one concept in order to solve such questions! [After that you can solve questions in which we are asked to find displacement, velocity or acceleration.]

• Work done by tension force = Zero

We know that work done is defined as the dot product of force and displacement.

Remember the following three formulas :-

1. T • d = 0
2. T • v = 0 (By diff. 1st equation)
3. T • a = 0 (By diff. 2nd equation)

Tension on block B (T₁) = T cos60°

Tension on block A (T₂) = T cos37°

• Velocity of block B = v₁
• Velocity of block A = v₂

By substituting the values in second equation;

➙ $\sf\sum$ T • v = 0

➙ (T₁ • v₁) + (T₂ • v₂) = 0

➙ (-T cos60° × 10) + (T cos37° × v₂) = 0

➙ 10 cos60° = v₂ cos37°

➙ 10 × 1/2 = v₂ × 4/5

➙ v₂ = 25/4

➙ v₂ = 6.25 m/s

Answer 2

Concept:

• Considering the strings and the mass of the pulley is massless, since there masses are not given.

• so, according to massless strings condition:

1. whole string possess the same tension.
2. every segment will be associated with same velocity or acceleration on extension.
3. ★★so, if the string is moving with some velocity from one end in horizontal direction, no matter of the masses, the other end will have the same extension/ velocity in horizontal direction.

Solution:

velocityof A = v (whole along the string)

velocity of B = 10 m/s (only in x-dirn)

horizontal velocity will same in both end

• vcos37° = 10
• v(4/5) = 10
• v= 50/4
• v = 12.5 m/s

☆☆ means the velocity of A will be in some oblique direction along the string which has its horizontal component as 10m/s.

• we can say that tension in the string of vertical component in the case of A has not totally get cancel out by mg thats why it moves upwards.
• whereas in case of B y-axis motion is in eq. condition as no force for motion, results only in x-dirn.