A 58.0-kg man is riding an escalator in a shopping mall. The escalator moves the man at a constant velocity from ground level to the floor above, a vertical height of 3.70 m. What is the work done on the man by (a) the gravitational force and (b) the escalator?
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To calculate the work done on the man by the gravitational force, we need to use the formula:
Work = Force x Distance x cos(angle)
(a) The gravitational force can be calculated using:
Force = Mass x Gravity
Where:
Mass = 58.0 kg (given)
Gravity = 9.8 m/s^2 (acceleration due to gravity)
Force = 58.0 kg x 9.8 m/s^2
Force = 568.4 N
Distance = 3.70 m (given)
Angle = 0° (as the force and displacement are in the same vertical direction)
Now we can substitute the values into the formula:
Work = 568.4 N x 3.70 m x cos(0°)
Work = 568.4 N x 3.70 m x 1
Work = 2102.8 Joules
Therefore, the work done on the man by the gravitational force is 2102.8 Joules.
(b) Since the escalator moves the man at a constant velocity, the net force acting on the man is zero. This means that the work done by the escalator is also zero.
Therefore, the work done on the man by the escalator is zero.
To find the work done on the man by the gravitational force and the escalator, we need to use the formula for work:
Work = Force × Distance × Cosine(angle)
(a) The work done by the gravitational force on the man:
The force due to gravity is equal to the weight of the man, which is given by:
Weight = mass × gravitational acceleration
Weight = 58.0 kg × 9.8 m/s^2
Weight = 568.4 N
The distance the man is lifted is 3.70 m.
The angle between the direction of the force (gravity) and the direction of displacement (vertical) is 0 degrees (cosine of 0 is 1).
Using the work formula, we can calculate:
Work_gravity = 568.4 N × 3.70 m × Cosine(0)
Work_gravity = 2102.8 J
Therefore, the work done by the gravitational force on the man is 2102.8 joules (J).
(b) The work done by the escalator on the man:
Since the escalator is moving the man at a constant velocity, there is no net force acting in the direction of displacement. Therefore, the work done by the escalator is zero.
Hence, the work done by the escalator on the man is 0 joules (J).
In summary,
(a) The work done on the man by the gravitational force is 2102.8 joules (J).
(b) The work done on the man by the escalator is 0 joules (J).
a. Work = = M*g*h = 58 * 9.8 *3.7 = 2103 J.
b. Work = M*g*h.