Calculating Tension Needed to Lift 1400 kg Car

[mortho]

Homework Statement

How much tension must a rope withstand if it is used to accelerate a 1400 kg car vertically upward at 0.50 m/s2?

Homework Equations

Fg=mg F=ma

The Attempt at a Solution

So far i know Fg=13720 and the Fnet is 700 so I'm not sure but do i subtract 700 from 13720?

 

[Mindscrape]

Would it make sense, physically, if the tension force were less than the gravitational force, as you are saying?

 

[ogb p]

I would approach this problem by first identifying the relevant equations and variables. The given information states that a rope is used to accelerate a 1400 kg car vertically upward at 0.50 m/s2, and we are asked to find the tension needed to accomplish this.

The relevant equations are Newton's second law (F=ma) and the equation for gravitational force (Fg=mg). In this case, the tension in the rope would be the net force (Fnet) acting on the car.

Using Newton's second law, we can calculate the net force required to accelerate the car upward:

Fnet = ma = (1400 kg)(0.50 m/s2) = 700 N

Next, we can use the equation for gravitational force to calculate the weight of the car (Fg):

Fg = mg = (1400 kg)(9.8 m/s2) = 13720 N

Since the rope must withstand the weight of the car (Fg) as well as the force needed to accelerate it (Fnet), the total tension required would be the sum of these two forces:

Tension = Fnet + Fg = 700 N + 13720 N = 14420 N

Therefore, the tension needed to lift the 1400 kg car at 0.50 m/s2 would be 14420 N. It is important to note that this is the minimum tension required, as there may be other factors (such as friction) that could increase the tension needed.