Find the forces exerted by the two supports of a 4.0m, 50-kg diving board when a 60-kg woman stands at its end. The two supports are 0.8m apart. This time consider the mass of the diving board.
x1= 0.8m -the distance between supports.
x2= 1.2 m - the distance between the right-hand support anf the center of mass of the board,
x3 =3.2 m –the distance between the right-hand support and the diver.
m1= 50 kg, m1•g = 490 N,
m2= 60 kg, m2•g = 588 N.
F1 is the downward force on the left-hand support,
F2 is the upward force on the right-hand support.
Three torques act about the right support
τ1=+F1•x1,
τ2 = - m1•g•x2,
τ3 = - m2•g•x3,
Σ τ= τ1 +τ2 +τ3 = 0,
F1•0.8 - 490•1.2 - 588•3.2 = 0,
F1=(490•1.2 + 588•3.2)/0.8 =3087 N
ΣF = - F1 + F2 - m1•g - m2•g = 0,
-3087+F2-490-588 =0
F2 = 3087+ 490+588=4165 N
To find the forces exerted by the two supports on the diving board, we need to analyze the forces acting on the system. In this case, we have the weight of the diving board, the weight of the woman, and the reaction forces exerted by the two supports.
1. Weight of the diving board:
The weight of an object is given by the formula W = m * g, where W is the weight, m is the mass, and g is the acceleration due to gravity. The mass of the diving board is given as 50 kg, and the acceleration due to gravity is approximately 9.8 m/s². Therefore, the weight of the diving board is W1 = 50 kg * 9.8 m/s².
2. Weight of the woman:
Similarly, we can calculate the weight of the woman using her mass and the acceleration due to gravity. The mass of the woman is given as 60 kg, so the weight of the woman is W2 = 60 kg * 9.8 m/s².
3. Reaction forces from the supports:
The total force exerted by the supports in the vertical direction must balance the combined weight of the diving board and the woman. Since the two supports are 0.8 m apart, and assuming the diving board is uniform, each support should exert half of the total force.
Let's calculate the forces exerted by each support:
Force1 = (W1 + W2) / 2
Force2 = (W1 + W2) / 2
Substituting the values we calculated earlier for W1 and W2, we can find the forces for each support.
Please note that we have assumed the diving board is at rest and in equilibrium. If there are any horizontal forces acting on the diving board, they should also be considered in the analysis.