A 70 kg man stands at the end of a 12 m long platform. The end opposite
to the man rests on the edge of a wall, and a support column is located a
distance d = 3 m from the end with the man. The platform itself has a mass
of 300 kg. (a) How much weight does the column support? (That is, what is
the normal force on the platform from the column?) (b) How massive must
the man be in order for the opposite end of the platform to lift off of the
wall?
A sturdy wooden board, 4.0 meters long and with a mass of 32 kg, rests on two supports (labeled L and R) placed 1.2 m from each end as shown in the figure below. (a) Suppose that a man with a mass of 60 kg stands at the center of
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To solve this problem, we need to consider the forces acting on the platform.
(a) To calculate the weight supported by the column, we need to find the net force acting on the platform in the vertical direction.
First, let's determine the forces acting on the platform:
1. Weight of the platform: This force is acting downwards and is equal to the mass of the platform (300 kg) multiplied by the acceleration due to gravity (9.8 m/s^2). So, the weight of the platform is 300 kg * 9.8 m/s^2 = 2940 N (Newtons).
2. Weight of the man: This force is acting downwards due to the man's weight and is equal to the man's mass (70 kg) multiplied by the acceleration due to gravity (9.8 m/s^2). So, the weight of the man is 70 kg * 9.8 m/s^2 = 686 N.
3. Normal force from the column: This force is acting upwards from the column and supports the weight of the platform and the man.
Next, let's analyze the forces in the vertical direction:
1. Upwards forces: Normal force from the column.
2. Downwards forces: Weight of the platform and weight of the man.
At equilibrium, the net force acting in the vertical direction is zero. Therefore:
Net Force = Upwards force - Downwards force = 0.
Using this information, we can write an equation:
Normal force from the column - Weight of the platform - Weight of the man = 0.
To find the normal force from the column, we can rearrange the equation:
Normal force from the column = Weight of the platform + Weight of the man.
Substituting the given values, we have:
Normal force from the column = 2940 N + 686 N = 3626 N.
Therefore, the column supports a weight of 3626 N.
(b) To determine how massive the man must be for the opposite end of the platform to lift off the wall, we need to calculate the torque acting on the platform.
Torque is calculated as the force applied at a distance from a pivot point. In this case, the pivot point is the end resting on the wall.
The torque acting on the platform is given by:
Torque = Force x Distance.
The force causing the torque is the weight of the man, and the distance is the length of the platform.
Since the platform will lift off the wall when the torque becomes greater than or equal to zero, we can set up an equation:
Torque = Force x Distance = 0.
Substituting the given values, we have:
Force (weight of the man) x Distance (12 m) = 0.
We need the weight of the man to be zero in order for the opposite end to lift off the wall. Therefore, the man must have no mass (0 kg).
In conclusion, for the opposite end of the platform to lift off the wall, the man must have zero mass.