Solving Part (a) of Lamp Mass in Descending Elevator w/ Deceleration of 1.4 m/s2

[shell4987]

Homework Statement

A lamp hangs vertically from a cord in a descending elevator that decelerates at 1.4 m/s2. (a) If the tension in the cord is 56 N, what is the lamp's mass? (b) What is the cord's tension when the elevator ascends with an upward acceleration of 1.4 m/s2?

Homework Equations

T-mg=ma

The Attempt at a Solution

I got part (b) to be 56 N and that was correct but then I used the formula... but I don't know how to solve for mass for part (a) when there are two masses in the equation above, I know T to be 56N and g to be 9.8m/s squared also a to be 1.4m/s squared... Can anyone help me out? I'm confused.

 

[Doc Al]

Just rearrange your initial equation:
T-mg=ma

Thus:
T = mg + ma = m(g +a)

You take it from here.

 

[m2003]

I would approach this problem by first identifying the known quantities and the equations that can be used to solve for the unknown quantity. In this case, the known quantities are the tension in the cord (T = 56 N), the acceleration (a = 1.4 m/s2), and the gravitational acceleration (g = 9.8 m/s2). The unknown quantity is the mass of the lamp (m).

To solve for the mass, we can use the equation T - mg = ma. We know the values of T, a, and g, so we can rearrange the equation to solve for m:

m = (T - ma)/g

Substituting the known values, we get:

m = (56 N - (1.4 m/s2)(m))/9.8 m/s2

Simplifying, we get:

m = (56 N - 1.4 m/s2 * m)/9.8 m/s2

m = (56 N - 1.4 m/s2 * m)/9.8 m/s2

m = (56 N - 1.4 * m)/9.8

Multiplying both sides by 9.8, we get:

9.8m = 56 N - 1.4m

Adding 1.4m to both sides, we get:

11.2m = 56 N

Dividing both sides by 11.2, we get:

m = 56 N / 11.2

m = 5 kg

Therefore, the mass of the lamp is 5 kg.

It is important to note that in this problem, the mass of the cord is negligible compared to the mass of the lamp. If the mass of the cord was significant, it would need to be taken into account in the calculation.