Imagine a right-angle triangle with angle θ = 40o on the left. The serves as an increasing slope. On the slope is

an object of mass m1= 340 g on an inclined surface. The angle of the inclined surface is θ = 40o with the horizontal. The object m1 is connected to a second object of mass m2 = 338 g on the adjacent horizontal surface.

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Further, an external force of magnitude ІFextІ = 5.5 N is exerted on the object of mass m1. We observe both objects to accelerate. Assuming that the surfaces and the pulley are frictionless, and the pulley and the connecting string are massless, what is the tension in the string connecting the two objects?

my values were θ = 40o, m1 = 397g, m2 = 314g, |Fext| = 4.7 N...

i got my answer as 0.971 N

http://www.jiskha.com/display.cgi?id=1254845390

To find the tension in the string connecting the two objects, we can use Newton's second law of motion.

Step 1: Determine the forces acting on each object individually.

Object m1 on the inclined surface:
- The force of gravity acting vertically downwards (mg), where m is the mass of m1 and g is the acceleration due to gravity.
- The force applied by the external force (Fext) acting along the incline.
- The tension force in the string (T) acting upwards.

Object m2 on the horizontal surface:
- The force of gravity acting vertically downwards (mg), where m is the mass of m2 and g is the acceleration due to gravity.
- The tension force in the string (T) acting towards the pulley.

Step 2: Find the acceleration of each object.

Since the surfaces and the pulley are frictionless, the tension force (T) will be the same for both objects. Therefore, we can equate the forces of both objects in the y-direction (perpendicular to the inclined surface) to find the acceleration.

For object m1:
mg*sinθ - T = m1*a1

For object m2:
T = m2*a2

Step 3: Relate the accelerations of both objects using the pulley.

Given that the pulley is massless and frictionless, the accelerations of both objects will be the same.

a1 = -a2 (opposite direction due to the string)

Step 4: Solve the equations simultaneously.

Substitute a2 = -a1 into the equation for object m2:

T = m2*(-a1)

Substitute T = m2*(-a1) into the equation for object m1:

mg*sinθ - m2*(-a1) = m1*a1

Simplify the equation:

mg*sinθ + m2*a1 = m1*a1 + m2*a1

Solve for a1:

a1 = (mg*sinθ) / (m1 + m2)

Step 5: Find the tension in the string.

Substitute a1 into the equation for object m2:

T = m2*(-a1)

T = -m2*(mg*sinθ) / (m1 + m2)

Finally, we have found the tension in the string connecting the two objects.