What is the force exerted on a man weighing 700 N by the elevator floor when the elevator is accelerating upward at 4 m/s²?
The force exerted on a man by the elevator floor can be calculated using the formula F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, the man's weight is given as 700 N and the acceleration of the elevator is 4 m/s².
To find the force, we first need to determine the man's mass. We can find the mass using the formula: mass (m) = weight (W) / acceleration due to gravity (g). Given that W = 700 N and g = 9.81 m/s², we can calculate the man's mass as follows:
m = 700 N / 9.81 m/s² = 71.35 kg
Next, we can find the force exerted by the elevator floor using F = ma, with the calculated mass (m) and the acceleration (a) provided:
F = 71.35 kg × 4 m/s² = 285.4 N
The closest answer to 285.4 N is 290 N. Therefore, the force exerted on the man by the elevator floor is approximately 290 N.
Understanding Force Exerted on Man in Elevator
Force: In physics, force is a push or pull upon an object resulting from the object's interaction with another object. It is a vector quantity, meaning it has both magnitude and direction. The SI unit of force is the Newton (N).
Mass and Weight: Mass is a measure of the amount of matter in an object, while weight is the force acting on an object due to gravity. The weight of an object is equal to the mass of the object multiplied by the acceleration due to gravity (W = mg).
Acceleration: Acceleration is the rate of change of velocity with respect to time. When the elevator accelerates upward at 4 m/s², it means the velocity of the elevator is increasing by 4 meters per second every second.
Calculation Process: We first calculated the man's mass by dividing the weight (700 N) by the acceleration due to gravity (9.81 m/s²) to get approximately 71.35 kg. Then, using the formula F = ma, we found the force exerted by the elevator floor on the man to be approximately 285.4 N. The closest answer provided is 290 N.
In conclusion, when a man weighing 700 N is in an elevator that is accelerating upward at 4 m/s², the force exerted on him by the elevator floor is approximately 290 N. This calculation showcases the relationship between mass, acceleration, and force in a real-world scenario.