Mechanics- connected particles

• MHB
• Shah 72
In summary, The tension in the lift cable can be calculated using the scalar equations: for (a) T-320g=320a, for (b) T-320g=0, and for (c) 320g-T=320a. In case (a), the acceleration is upward at 0.3m/s^2, for (b) there is no acceleration, and for (c) the acceleration is downward at 0.3m/s^2.
Shah 72
MHB
A crate of mass 20 kg is put into a lift. The mass of the lift is 300kg. Find the tension in the lift cable.
a) when the lift accelerates upwards at 0.3m/s^2
b) when the lift travels at constant speed
c) when the lift accelerates downwards at 0.3m/s^2
For (a) is it T- W-w= ( M+m) a
Where T is tension of the cable, W is the weight of the lift and w is the weight of the mass.
I don't know how to calculate (b) and (c)

Shah 72 said:
A crate of mass 20 kg is put into a lift. The mass of the lift is 300kg. Find the tension in the lift cable.
a) when the lift accelerates upwards at 0.3m/s^2
b) when the lift travels at constant speed
c) when the lift accelerates downwards at 0.3m/s^2
For (a) is it T- W-w= ( M+m) a
Where T is tension of the cable, W is the weight of the lift and w is the weight of the mass.
I don't know how to calculate (b) and (c)
For a I did T-3000-200= 320×0.3
Iam getting 3296N
b) I did T-3000-206= 320×0.3, I get 3302, textbook ans for (b) is 3200 and for (a) its 3300N

scalar equations ... all use the magnitude of acceleration

(a) $T - 320g = 320a$
$a$ is upward

(b) $T - 320g = 0$
no acceleration, why?

(c) $320g - T = 320a$
$a$ is downward

skeeter said:
scalar equations ... all use the magnitude of acceleration

(a) $T - 320g = 320a$
$a$ is upward

(b) $T - 320g = 0$
no acceleration, why?

(c) $320g - T = 320a$
$a$ is downward
Second case is constant speed so a=0.

1. What is the definition of connected particles in mechanics?

Connected particles in mechanics refer to two or more objects that are physically connected or constrained to move together as a single system. This can include objects connected by a string, rod, or any other type of rigid or flexible link.

2. How are the forces and motion of connected particles related?

The forces acting on connected particles are directly related to their motion. According to Newton's second law of motion, the net force on an object is equal to its mass multiplied by its acceleration. In the case of connected particles, the net force is the sum of the individual forces acting on each particle, and their acceleration is the same since they are constrained to move together.

3. What is the difference between internal and external forces in connected particles?

Internal forces in connected particles are forces that act between the particles within the system. These forces do not affect the overall motion of the system, but rather the relative motion between the particles. External forces, on the other hand, are forces that act on the system as a whole and can change its motion.

4. How do you calculate the tension in a string connecting two particles?

The tension in a string connecting two particles can be calculated using Newton's second law of motion. The net force acting on the particles in the direction of the string must be equal to the mass of the particles multiplied by their acceleration. This net force is equal to the tension in the string.

5. Can connected particles be treated as a single object for calculations?

Yes, connected particles can be treated as a single object for calculations as long as the forces acting on the individual particles are taken into account. This is because the particles are constrained to move together and their motion is dependent on the forces acting on the system as a whole.

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