Question

** You pull a rope oriented at a 37° angle above the horizontal. The other end of the rope is attached to the front of the first of two wagons that have the same 30-kg mass. The rope exerts a force of magnitude T1 on the first wagon. The wagons are connected by a second horizontal rope that exerts a force of magnitude T2 on the second wagon. Determine the magnitudes of T1 and T2 if the acceleration of the wagons is 2.0 m⁄s2.

Answer 1

Answer:

T2= 60 N and T1= 150,25 N

Explanation:

a free body diagram has to be done

Answer 2

The magnitude of the forces T1 and T2 if the acceleration is 2m/s² is 60N and 150.26N respectively.

Find the free body diagram attached. According to newton's second law;

$\sum F_x = ma_x$

∑Fx is the sum of applied force in the horizontal direction

m is the mass of the object

ax is the acceleration of the object

For the body of mass 30kg

∑T = ma

T2 = ma

T2 = 30 * 2

T2 = 60N

For the sum of force acting on the second body;

T1 cos θ - T2 = ma

T1 cos 37 - 60 = 30(2)

T1 cos 37 = 120

T1 = 120/cos37

T1 = 120/0.7986

T1 = 150.26N

This shows that the magnitude of the forces T1 and T2 if the acceleration is 2m/s² is 60N and 150.26N respectively.

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