Question

two part question)A 110-kg horizontal beam is supported at each end. A 320 kg piano rests a quarter of the way from left end. What is the vertical forceon each of the supports, FL and FR, left and right ends? (a) FL.! (b) FR No units on answer

Answer 1

a) FL = 2893.95 N

b) FR = 1324.35 N

Step-by-step explanation

The beam has a mass of 110 kg, so even before the piano is placed the ends of the beam support and initial force. The gravitational force (or weight) of the beam is:

This is the total weight of the beam. Each end is under half this force:

`F_(support)=(Fg)/(2)=539.55N`

Now we add the piano. Let's make a diagram to see the situation better:

The piano has a mass of 320kg. Its total weight is:

`Fg_(piano)=m_(piano)\cdot g=320\cdot9.81=3139.2N`

Since the piano is not at the middle of the beam, each end will not support the same weight.

The additional weight on the left support is:

`F_{\text{Lextra}}=(3)/(4)\cdot Fg_(piano)=2354.4N_{}`

So the total force on the left support is:

`F_L=2354.4N+539.55N=2893.95N`

In the same way, the rest of the piano's weight is supported by the right support:

`F_{\text{Rextra}}=(1)/(4)Fg_(piano)=784.8N`

And the total force supported by the right support is:

`F_R=784.8N+539.55N=1324.35N`