A tall strongman of mass m = 93 kg stands upon a scale while at the same time pushing on the ceiling in a small room.If the scale reads 1062 N (about 239 lb), what is the magnitude of the normal force that the ceiling exerts on the strongman?
To find the magnitude of the normal force that the ceiling exerts on the strongman, we need to consider the forces acting on the strongman.
1. The force of gravity: The strongman's weight is given by the formula weight = mass x acceleration due to gravity. So, weight = m x g, where m is the mass (93 kg) and g is the acceleration due to gravity (9.8 m/s^2). Therefore, the force of gravity on the strongman is Fg = m x g.
2. The force exerted by the scale: The scale reading (1062 N) represents the force exerted by the scale on the strongman. The scale measures the normal force, which is the force perpendicular to the surface it is placed upon. In this case, the scale provides us with the magnitude of the normal force exerted by the strongman on the scale. Since the strongman is at rest on the scale, the scale reading is equal in magnitude and opposite in direction to the normal force exerted by the scale on the strongman.
3. The force exerted by the ceiling: The strongman is pushing on the ceiling, creating a force exerted by the ceiling onto the strongman. Let's call this force Fc.
The equilibrium condition states that the sum of all forces acting on an object is zero, so we can write:
Fg - Fc - Fs = 0,
where Fs is the force exerted by the scale.
Since the scale reading is the magnitude of the force exerted by the strongman on the scale, we have Fs = 1062 N.
Therefore, we can rearrange the equation to solve for Fc:
Fc = Fg - Fs.
Substituting the values we know, we have:
Fc = (mass x acceleration due to gravity) - scale reading
= (93 kg x 9.8 m/s^2) - 1062 N.
Evaluating this expression, we get the magnitude of the normal force exerted by the ceiling on the strongman.
Note: Make sure to convert the pounds value to Newtons (1 lb = 4.448 N) if needed.