(Newton's 2nd & 3rd laws) finding mass

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In summary, a mass is suspended by two cables at angles of 30° and 60° with the ceiling. The first cable has a tension of 24.5 N and the second cable has a tension of 42.7 N. To find the mass, we use the formula m=Fnet/a and determine the vertical components of the two tensions, which are 21.21 N and 21.35 N. It is important to note that there are three forces acting on the mass, including the force of gravity and the two tension forces. The horizontal components of the two tensions are equal in magnitude.
  • #1
shamma
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A mass is hanged by 2 cables, the first makes 30° with the ceiling while the second makes 60° with the ceiling. Find the attached mass if the first tension is 24.5 N and the second tension is 42.7 N.

my way:
T1=24.5N θ=30
T2=42.7N θ= -60
m=?
m=Fnet/a

the ans should be (m=5.017 Kg)
 
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  • #2
How many forces act on the mass?
 
  • #3
3 forces
Fg and 2 tension forces
 
  • #4
Now find the vertical components of the two tensions.
 
  • #5
T1: 24.5 sin 60=21.21N
T2: 42.7 sin 30=21.35N
 
  • #6
shamma said:
T1: 24.5 sin 60=21.21N
T2: 42.7 sin 30=21.35N

If you draw a diagram you will notice that the above are the HORIZONTAL components.

(Incidentally, the horizontal components must be equal in magnitude)
 
  • #7
yes, your right.
 

FAQ: (Newton's 2nd & 3rd laws) finding mass

How do you find the mass of an object using Newton's 2nd law?

According to Newton's 2nd law of motion, the mass of an object can be determined by dividing the net force acting on the object by its acceleration. This can be represented by the equation F=ma, where F is the net force, m is the mass, and a is the acceleration. By rearranging the equation to solve for mass, we get m=F/a.

Can Newton's 2nd law be used to find the mass of an object at rest?

Yes, Newton's 2nd law can still be used to find the mass of an object at rest. In this case, the acceleration would be 0, and the equation would simplify to m=F/0, which is undefined. However, if we assume that the acceleration is negligible, the equation can still be used to estimate the mass of the object.

How does Newton's 3rd law relate to finding mass?

Newton's 3rd law states that for every action, there is an equal and opposite reaction. This means that when an object is exerting a force on another object, the second object is also exerting an equal and opposite force on the first object. In the context of finding mass, this means that the force applied to an object and the force exerted by that object are equal and can be used in Newton's 2nd law equation to find the mass.

Can Newton's 2nd law be used to find the mass of a moving object?

Yes, Newton's 2nd law can be used to find the mass of a moving object as long as the acceleration of the object is known. This can be determined by measuring the object's change in velocity over a certain time period. The mass can then be calculated using the equation m=F/a.

What units should be used when using Newton's 2nd law to find mass?

In order for the equation to be valid, the units for force should be in Newtons (N) and the units for acceleration should be in meters per second squared (m/s^2). The resulting unit for mass would then be in kilograms (kg).

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