I am having a lot of difficulty with this question. Thank you in advance for a thorough explanation!

Question

A student is doing a physics experiment with a pendulum, with a 2.8kg bob, in the car ride home from school. At one point during the ride the car is increasing speed at a rate of 4.8m/s². Assume the windows are rolled up.

How many forces are acting on the bob of the pendulum?

What is the magnitude of the net force?

What is the strength of the tension?

At what angle, θ, does the pendulum hold?

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Answer 1

A free body diagram would look like this:

W = mg = 2.8(9.81) = 27.47 N

T (tension) can be broken down into an x-component and a y-component. T_x = Tsin(θ) and T_y = Tcos(θ) (notice this is slightly different than a typical case where cosine is associated with the "x". Draw yourself a little triangle if you need to convince yourself this is correct.

Considering the sum of the forces:

∑F_x = ma and ∑F_y = 0

In the y-direction:

Tcos(θ) - W = 0

Tcos(θ) = W

Tcos(θ) = 27.47

In the x-direction:

Tsin(θ) = ma

Tsin(θ) = 2.8(4.8)

Tsin(θ) = 13.44

Now, divide the two equations. This might seem a little weird but since "Tcos(θ) = 27.47 then "Tcos(θ)" is exactly the same as "27.47" so another way to think about it is the divide Tsin(θ) = 13.44 by the same thing on both sides, you just choose to use the left side as "Tcos(θ)" and the right side as "27.47":

Tsin(θ)/Tcos(θ) = 13.44/27.47

The "T's" cancel and sin(θ)/cos(θ) = tan(θ) yielding:

tan(θ) = 13.44/27.47

tan(θ) = 0.4893

θ = tan^-1(0.4893)

θ = 26°

The "net force" is in the x-direction and so is 13.44 N

Using either Tcos(θ) = 27.47 or Tsin(θ) = 13.44 you can plug in θ and solve for the tension.