Question

You need to design an experiment to measure the free-fall acceleration. You have an inclined plane made of steel and several objects that you may place on the plane. The plane is fixed at 45°. You have a Teflon-coated block with a mass of 0.5 kg, a cart with steel wheels and a mass of 1.5 kg, and a steel box with a mass of 0.75 kg. You have a sonar device to measure the acceleration. You are to place one or more objects on the plane and measure their acceleration along the plane. Does it matter which object or objects you choose? If not, why not? If so, which would you use? Explain your answer.

Answer 1

Attached a diagram of the scheme described in the problem ..

To solve the problem we need to know the relationship between kinetic and normal force, so

$F_k=\mu_k F_N (1)$

Where

$\mu_k =$ coefficient of kinetic

$F_N=$  Normal force

We perform the sum of forces as well,

$\sum F_x = Ma$(2)

$a= Acceletarion$

For Normal Force in Y,

$F_N= Mgcos \theta$  (3)

The force in X,

$\sum F_x = Mgsin\theta - F_x$ (4)

Replacing in (4)

$Ma = Mgsin\theta - \mu_k F_N$

$Ma = Mgsin\theta - \mu_k F_N$

$Ma = Mgsin\theta - \mu_k Mg cos\theta$

$a= g(sin\theta-\mu_k cos\theta)$

In this way, it does not matter which object is chosen.