Equilibrium: Mass on an inclined plane held by a string, find the tension

In summary, To solve for the tension in the cable in this scenario, the equation T=MG cannot be used due to the presence of an angle. Instead, a free body diagram should be drawn and the parallel and perpendicular components of the gravitational force should be considered. The equation mg sinθ can be used to solve for the tension, but it is important to understand the problem conceptually in order to apply the correct equation for variations of this problem.
  • #1
Jujubee37
22
4
Homework Statement
A block of mass M = 6.2 kg is placed on a frictionless inclined plane that makes an angle of 40.4 deg with respect to the horizontal. The block is held in place by a massless string.

magnitude of normal force; 46.2700 N

Enter the magnitude of the tension T in the string.
Relevant Equations
Normally the equation I use is T=MG but in this case it doesn't work and I think it might be because of the angle.
6.2(9.8)=60.8 (incorrect)
46.2cos40.4= 35.2 (incorrect)
 
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  • #2
Jujubee37 said:
Relevant Equations:: Normally the equation I use is T=MG but in this case it doesn't work and I think it might be because of the angle.
That angle is key! Start by drawing yourself a free body diagram of all the forces acting on that block. Hint: Pay close attention to the force components parallel to the incline surface.
 
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  • #3
Doc Al said:
That angle is key! Start by drawing yourself a free body diagram of all the forces acting on that block. Hint: Pay close attention to the force components parallel to the incline surface.
If that is the case, would I used mg sinθ? I'm confused on what equation I should use.
 
  • #4
Jujubee37 said:
If that is the case, would I used mg sinθ? I'm confused on what equation I should use.
Yes, but try to think more generally about this problem so you can solve all sorts of variations without having to memorize what equation goes where.

What are the parallel and perpendicular components of the gravitational force acting on the block? (Parallel and perpendicular to the incline surface.)
 
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  • #5
Doc Al said:
Yes, but try to think more generally about this problem so you can solve all sorts of variations without having to memorize what equation goes where.

What are the parallel and perpendicular components of the gravitational force acting on the block? (Parallel and perpendicular to the incline surface.)
Yes thank you I have another problem so I will try to work at it your way. thanks x
 

1. What is equilibrium in a physical system?

Equilibrium refers to a state in which all forces acting on a system are balanced, resulting in no net movement or acceleration.

2. How does the mass of an object affect the equilibrium on an inclined plane?

The mass of an object affects the equilibrium on an inclined plane by increasing the force of gravity acting on the object, which must be balanced by an equal and opposite force, such as tension in a string.

3. How does the angle of the inclined plane affect the equilibrium of the system?

The angle of the inclined plane affects the equilibrium of the system by changing the direction and magnitude of the force of gravity acting on the object, which in turn affects the required tension in the string to maintain equilibrium.

4. What role does tension play in maintaining equilibrium on an inclined plane?

Tension plays a crucial role in maintaining equilibrium on an inclined plane by balancing the force of gravity acting on the object. The tension in the string must be equal to the component of the object's weight parallel to the inclined plane in order to keep the object from sliding down.

5. How can the tension in the string be calculated in this system?

The tension in the string can be calculated using the formula T = mg sinθ, where T is the tension, m is the mass of the object, g is the acceleration due to gravity, and θ is the angle of the inclined plane. This formula takes into account the forces acting on the object and ensures equilibrium is maintained.

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