A 160kg horizontal beam is supported at each end. A 330kg piano rests a quarter of the way from one end.
What is the vertical force on each of the supports?
To determine the vertical force on each of the supports, we need to consider the weight of the beam and the piano.
Step 1: Find the weight of the beam.
The weight of the beam can be calculated using the formula:
Weight = mass x acceleration due to gravity
Given that the mass of the beam is 160 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight of the beam as follows:
Weight of the beam = 160 kg x 9.8 m/s^2 = 1568 N
Step 2: Find the weight of the piano.
The weight of the piano can be calculated using the same formula:
Weight = mass x acceleration due to gravity
Given that the mass of the piano is 330 kg, we can calculate the weight of the piano as follows:
Weight of the piano = 330 kg x 9.8 m/s^2 = 3234 N
Step 3: Determine the vertical force on each support.
Since the piano rests a quarter of the way from one end, it can be considered as exerting equal horizontal forces on both supports.
Hence, the total horizontal force exerted by the piano is given by:
Total Horizontal Force = Weight of the piano / 2
= 3234 N / 2
= 1617 N
Considering the equilibrium of the beam, the vertical force on each support can be determined by dividing the total weight of the beam and piano equally between the two supports and adding the vertical force exerted by the piano.
Vertical Force on each support = (Weight of the beam + Weight of the piano) / 2 + (Weight of the piano / 2)
= (1568 N + 3234 N) / 2 + 1617 N / 2
= 4802 N / 2 + 1617 N / 2
= 2401 N + 808.5 N
= 3209.5 N
Therefore, the vertical force on each of the supports is approximately 3209.5 N.
To find the vertical force on each of the supports, we need to consider the weight distribution of the beam and the piano.
First, let's calculate the weight of the beam. The weight of an object is given by the formula W = m * g, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2). In this case, the beam has a mass of 160 kg, so its weight is W_beam = 160 kg * 9.8 m/s^2 = 1568 N.
Next, we need to calculate the weight of the piano. Since the piano rests a quarter of the way from one end, it means it is closer to one of the supports. Let's assume it is closer to support B. Since the beam is symmetrical, the weight of the piano is evenly distributed between support A and support B. Therefore, each support will bear half the weight of the piano.
The weight of the piano is given by W_piano = m_piano * g, where m_piano is the mass of the piano (330 kg). So, W_piano = 330 kg * 9.8 m/s^2 = 3234 N.
Since the piano rests a quarter of the way from one end and the beam is evenly distributed, we can calculate the distance d between the piano and each support. Let's assume the length of the beam is L. Since the piano is a quarter of the way from one end, we have d = L/4.
Now, to find the vertical force on each support, we can sum up the weights supported by each support.
Support A:
The vertical force on support A consists of the weight of the beam and half the weight of the piano.
Vertical force on support A = W_beam + (1/2) * W_piano
Support B:
The vertical force on support B consists of the weight of the beam and half the weight of the piano.
Vertical force on support B = W_beam + (1/2) * W_piano
Substituting the values, we have:
Vertical force on support A = 1568 N + (1/2) * 3234 N
Vertical force on support B = 1568 N + (1/2) * 3234 N
To get the exact values, calculate each expression:
Vertical force on support A = 1568 N + (1/2) * 3234 N = 1568 N + 1617 N = 3185 N
Vertical force on support B = 1568 N + (1/2) * 3234 N = 1568 N + 1617 N = 3185 N
Therefore, the vertical force on each of the supports A and B is 3185 N.
Fr=5N
I'll choose to place the piano 1/4 way from the right end
Fr= force right
Fl=force left
Fr+Fl-W-mg=0 where mg is the weight of the beam, W is the weight of the piano
(The sum of the forces in the vertical direction is zero because nothing is moving)
Then sum of the torques about any point will also be zero, because the beam is stationary. The weight of the beam acts halfway down the plank. The torque about the right end:
W*L/4+mgL/2-Fl*L=0
solve for Fl, then use Fr+Fl-W-mg=0 to solve for Fr