A standard man uses crutches. The crutches each make an angle of 25 degrees with the vertical. Half the standard man's weight is supported by the crutches; Assuming the standard man is motionless, find the magnitude of the force supported by each crutch.
on the y-component:fcos60+fcos60=1/2w 2fcos60=1/2w f=1/2w
To solve this problem, we need to understand the forces acting on the man and the crutches.
First, let's consider the forces acting on the man. We know that half of the man's weight is supported by the crutches, while the other half is supported by his legs. Since the man is motionless, the net force acting on him must be zero. Thus, the force supported by each crutch is equal to half of the man's weight.
To find the magnitude of the force supported by each crutch, we need to find the weight of the standard man. The weight of an object can be calculated using the formula:
Weight = Mass x Acceleration due to Gravity
The average mass of a standard man is around 70 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore, we can calculate the weight of the standard man as follows:
Weight = 70 kg x 9.8 m/s^2 = 686 N
Since half of the man's weight is supported by each crutch, the magnitude of the force supported by each crutch is:
Force supported by each crutch = 686 N / 2 = 343 N
Therefore, each crutch supports a force of 343 Newtons.