physics word problem (newton's laws)?

Question

the cable supporting a 2100 kg elevator has a max strength of 21750N. What maximum acceleration can it give the elevator without breaking?

the answer is.557 m/s^2, but how do you get that?

Answer 1

Max. Tension=21750N
Gravitational force=2100*9.8N
Therefore acceleration=(21750-20580)/2100
=1170/2100
=0.557m/s^2

Answer 2

When the elevator is at rest What do you think is the tension in th ecable supporting it. It is T = 2100x9.8 = 20580 N. This is the force with which earth attracts the elevator and the elevator is at rest. So there must be some equal force acting on the elevator upwards so that the net force is zero or acceleration is zero. This is then the tension in the cable supporting it. If the elevator descends with acceleration a < g then the net force acting on the elevator must be ma acting downwards. So Tension in the cable which acts upwards must be ma less than mg force exertyed by the earth on th elelvator. Mathematically

Mg - T = Ma or T = M(g-a) So T is less than the maximum tension the cable can stand before it breaks. If the elevator ascends with an acceleration a then T must be greater than Mg by Ma. Or mathematically, T = Mg + Ma or T = M (g+a). We can get the maximum acceleration of the elevator going upwards
by substituting T = 21750 N and Mg = 20580 N

So we have Ma = 1170 N = (21750 - 20580 ) or a(maximum)

is given by,

a = 1170 / 2100 m/s^2 =0.557 m/s^2

Answer 3

The cable tension, T, is divided between supporting the weight, W, and the force, F, devoted to accelerating the mass.

T = W + F

Weight is given by W = m*g. By Newton's 2nd, F = m*a. At the maximum safe acceleration, T = 21750N. So again

T = W + F
21750N = 2100 kg*9.8 m/s^2 + 2100 kg*a
21750 kg*m/s^2 = 20580 kg*m/s^2 + 2100 kg*a
So
a = 1170 kg*m/s^2 / 2100 kg = .557 m/s^2

I was surprised that using 10 versus 9.8 for g made such a difference. But it did.

Regarding Inquirer's answer: it's when the car accelerates upward that the tension is increased.

Answer 4

When the elevator accelerates downward, the force downward will add to its weight, causing additional tension in the cable.

When elevator is at rest, the tension in the cable = 2100*9.8 N = 20580 N

The additional tension the cable can bear = 21750 - 20580 = 1170 N

If this is the maximum excess tension allowed over the elevator's weight, then this is the maximum force that can be exerted by the motor that accelerates the elevator.

Max acceleration permissible = 1170 N / 2100 Kg = 0.557 m/s2

Answer 5

the forces that the elevator experts : T , P
T - P = ma
=> a = (T-P)/m = (T - mg)/m
the maximum acceleration is
a = (T - mg)/m = (21750 - 2100 * 10)/2100 = 0.357 m/s^2

Answer 6

a= 0.357 m/ s'2

Answer 7

uhmm
i think i gonna take the stairs