A man of mass 82 kg is using crutches. the crutches make an angle of 26 degrees with the vertical. Half the person's weight is supported by the crutches. Assuming that the person is at rest, find the magnitude of the force supported by each crutch.
the way i did this question was first i divided the weight by 2 since only half the weight is supported by the crutches and drew the free body diagram according to that. Now the force of the crutches is at an angle so we have to use vector components. I just used the y component of this force which was (F_T)(cos26). Also, the force of gravity is also acting on the body's weight, which came out to be: F_g = (41)(-9.8).
So,
Fnet y = (F_g) + (F_T)(cos26)
i got my answer for F_T to be 447 N.
Can someone please confirm if this is the right way to do this question and whether this answer is correct? Thanks in advance!
You have the good approach in isolating the free-body diagram, and taking advantage of symmetry.
The answer is correct.
Good work!
SO is the answer for each of the crutches 45.243N?
Can you elaborate on that. I still don't know how you calculated and got 447 N
Yes, your approach to solving the problem and your answer are correct!
To find the magnitude of the force supported by each crutch, you correctly divided the person's weight (82 kg) by 2 since only half of it is supported by the crutches. This gives us a weight of 41 kg.
Next, you drew a free body diagram and considered the forces acting on the person. The force of gravity (F_g) acts vertically downward with a magnitude of (41 kg)(-9.8 m/s^2), which you correctly calculated as F_g = -401.8 N (remember to include the negative sign since it acts in the opposite direction).
The force supported by the crutches can be divided into vertical and horizontal components. Since the crutches make an angle of 26 degrees with the vertical, you correctly used the vertical component of the force, which is F_T * cos(26 degrees). Let's call this component F_T_y.
Since the person is at rest, the net force in the vertical direction must be zero. Therefore, we can write:
F_T_y + F_g = 0
Plugging in the values we have:
F_T * cos(26 degrees) - 401.8 N = 0
Rearranging this equation, we can solve for F_T:
F_T = 401.8 N / cos(26 degrees)
Calculating this, we get F_T ≈ 447 N, which matches your answer.
So, your method and answer are correct! Well done!