We consider a man of mass m = 85 kg as shown in the figure below using crutches. The crutches each make an angle of è = 26o with the vertical. Half of the person's weight is supported by the crutches, the other half is supported by the normal forces acting on the soles of the feet. Assuming that the person is at rest, find the magnitude of the force supported by each crutch.
Express the result in the unit N and to three significant figures.
To find the magnitude of the force supported by each crutch, we will need to analyze the forces acting on the person.
Let's start by drawing a free-body diagram of the person. We have a downward force due to the person's weight acting at the center of mass, positioned vertically downward. This force can be represented by the equation:
Weight = mass * acceleration due to gravity
Weight = m * g
Since half of the person's weight is supported by the crutches and the other half by the normal forces acting on the soles of the feet, each crutch must support half of the person's weight. Therefore, the magnitude of the force supported by each crutch is:
Force per crutch = Weight / 2
Next, we need to find the weight of the person. Given that the mass of the person is 85 kg and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the weight as follows:
Weight = 85 kg * 9.8 m/s^2
Weight ≈ 833 N (rounded to three significant figures)
Now, we can find the magnitude of the force supported by each crutch by dividing the weight by 2:
Force per crutch = 833 N / 2
Force per crutch ≈ 416.5 N (rounded to three significant figures)
Therefore, the magnitude of the force supported by each crutch is approximately 416.5 N.