1. A guy is doing push ups, the length of the guy is 1.5 m, centre of mass is 0.9 m from the legs. He stops during the push up and holds the position in such a manner that his bent arm forms a 90 degree angle. Mass of the man is 50 kg. Find the force of the floor acting on both hands
2. A person lying on a plank with both ends on scales, with length 2 m and unknown centre of mass. His head side scale read F1=349 N and his foot side scaled reads F2=588 N. Mass of plank is negligible. Calculate the mass of the person and the centre of mass.
3. Draw a graph comparing centripetal acceleration vs angular velocity. (Just have to draw an exponential graph, right side half of an upward facing parabola)
To solve these problems, we'll be using the principles of torque, equilibrium, and centripetal acceleration. Let's go through each question and explain how to get the answer.
1. To find the force of the floor acting on both hands during the push-up, we'll consider the torque about the center of mass. The torque due to the weight acting at the center of mass and the torque due to the force of the floor acting on both hands must balance each other.
The torque due to the weight acting at the center of mass (mg) can be calculated as torque = force x distance = mg x distance. In this case, the distance is 0.9 m. So, the torque due to the weight is 50 kg x 9.8 m/s^2 x 0.9 m.
Since the man is at a 90-degree angle, the torque due to the floor forces on both hands must also be equal to the torque from the weight. So, the force of the floor acting on both hands would be torque / distance.
Plug in the values to calculate the force of the floor acting on both hands.
2. In this problem, we need to find the mass of the person and the center of mass. Since the plank is in equilibrium, the sum of the forces must be zero. The forces acting on the plank are the weight of the person (mg) and the normal forces on each end (F1 and F2).
The sum of the forces in the vertical direction gives us F1 + F2 - mg = 0. Substitute the given values for F1 and F2 into the equation.
To find the mass of the person, isolate the mass term in the equation.
To find the center of mass, we'll use the principle of mechanical equilibrium, which states that the sum of the torques around any point must be zero. We can take either end of the plank as the reference point. The torque due to the weight of the person is mg x (distance from the reference point to the center of mass), and the torque due to the normal forces is F1 x (distance from the reference point to F1) and F2 x (distance from the reference point to F2).
Since the plank is in equilibrium, the torques must balance each other. Set up the equation using the given values of F1 and F2 and solve for the distance from the reference point to the center of mass.
3. The graph comparing centripetal acceleration (a) and angular velocity (ω) is an upward-facing parabolic curve. As angular velocity increases, centripetal acceleration also increases, but at a decreasing rate.
To draw the graph, plot the values of centripetal acceleration (a) on the y-axis and angular velocity (ω) on the x-axis. As ω increases, start with a small positive value of a and gradually increase it. The rate at which a increases should decrease as ω increases, resulting in the upward-facing parabolic curve.