Because it asks for the man's power output, i.e. the rate at which the man does work against gravity. You have calculated the rate at which gravity does work on the man.Mohmmad Maaitah said:
The terms positive and negative preceding "work" are meaningless if you do not specify the force that does the work. When the body is lifted you say that the body has gained potential energy (correct) and you conclude "hence positive work." That's debatable. There is no default force that does work. The correct conclusion is "hence the lifting force does positive work and gravity does negative work." In this case the lifting force is provided by the Marine. The Marine's power output is positive at the expense of biochemical power generated in the Marine's muscles.Lnewqban said:
When an object is raised the vertical displacement vector ##\vec d## forms an angle of 180° with the force of gravity ##\vec F=m\vec g##. The work done by gravity on the raised object is $$W_g=\vec F\cdot \vec d=Fd\cos(180^{\circ})=Fd(-1)<0.$$ If the object is raised at constant speed, its kinetic energy does not change. By the work-energy theorem the work done by the net force must be zero, therefore the work done by the raising force is the negative of the work done by gravity, i.e. the raising force does positive work on the object.Lnewqban said:
Clear now, professor.kuruman said:
The work done by gravity is the energy transferred by the gravitational force when an object moves in the direction of the gravitational force. It is calculated as the product of the gravitational force, the displacement of the object, and the cosine of the angle between the force and the displacement vector.
The minus sign appears in the work done by gravity when considering the work done by an external force opposing gravity, such as lifting an object upwards. In this case, the gravitational force and the displacement are in opposite directions, resulting in a negative value for the work done by gravity.
When an object moves vertically, the work done by gravity can be calculated using the formula: \( W = mgh \), where \( W \) is the work done by gravity, \( m \) is the mass of the object, \( g \) is the acceleration due to gravity, and \( h \) is the vertical displacement. If the object is moving upwards, the work done by gravity is negative, and if it is moving downwards, the work is positive.
A positive work done by gravity indicates that gravity is doing work on the object, typically when the object is moving downwards. A negative work done by gravity indicates that an external force is doing work against gravity, such as when lifting an object upwards.
The angle of displacement affects the work done by gravity through the cosine term in the work formula. When the displacement is directly in the direction of the gravitational force (downwards), the angle is 0 degrees, and the work done by gravity is maximal and positive. When the displacement is directly opposite to the gravitational force (upwards), the angle is 180 degrees, and the work done by gravity is negative.