An elevator accelerates upward at 1.2 m/s^2
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The acceleration of gravity is 9.8 m/s^2
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What is the upward force exerted by the floor of the elevator on a(n) 52 kg passenger?
Answer in units of N.
F = Mg + Ma = 52*9.8 + 52*1.2 =
Well, this is an uplifting question! Let's crunch some numbers.
To find the upward force exerted by the floor of the elevator on the passenger, we need to calculate the net force acting on the passenger.
The net force can be found using Newton's second law, which states that force equals mass multiplied by acceleration:
Net force = mass × acceleration
Given:
Mass (m) = 52 kg
Acceleration (a) = 1.2 m/s^2
Plugging in the values, we get:
Net force = (52 kg) × (1.2 m/s^2)
Calculating this, we find:
Net force = 62.4 N
So, the upward force exerted by the floor of the elevator on the 52 kg passenger is a whopping 62.4 Newtons! That's a force to be reckoned with!
To solve this problem, we need to calculate the net force acting on the passenger.
The force exerted by the floor of the elevator on the passenger can be represented as F_floor. Additionally, the force due to the acceleration of the elevator can be represented as F_acceleration, and the force of gravity acting on the passenger can be represented as F_gravity.
The net force acting on the passenger is the sum of these forces:
F_net = F_floor + F_acceleration + F_gravity
Now, let's calculate each force:
1. Force exerted by the floor of the elevator on the passenger (F_floor):
The force exerted by the floor of the elevator on the passenger is equal to the passenger's weight. The weight of an object is given by the formula:
F_weight = mass * acceleration due to gravity (g)
Substituting the given values:
F_weight = 52 kg * 9.8 m/s^2
2. Force due to the acceleration of the elevator (F_acceleration):
The force due to the acceleration of the elevator is given by the following formula:
F_acceleration = mass * acceleration
Substituting the given values:
F_acceleration = 52 kg * 1.2 m/s^2
3. Force of gravity acting on the passenger (F_gravity):
The force of gravity on an object is given by the formula:
F_gravity = mass * acceleration due to gravity (g)
Substituting the given values:
F_gravity = 52 kg * 9.8 m/s^2
Now, let's calculate the net force:
F_net = F_floor + F_acceleration + F_gravity
= F_weight + F_acceleration + F_gravity
Substituting the calculated values:
F_net = (52 kg * 9.8 m/s^2) + (52 kg * 1.2 m/s^2) + (52 kg * 9.8 m/s^2)
Simplifying,
F_net = (499.6 N) + (62.4 N) + (509.6 N)
= 1071.6 N
Therefore, the upward force exerted by the floor of the elevator on the 52 kg passenger is 1071.6 N.
To find the upward force exerted by the floor of the elevator on the passenger, we need to consider the two forces acting on the passenger: the force due to acceleration and the force due to gravity.
First, let's calculate the force due to acceleration. The upward force exerted on the passenger due to acceleration is given by Newton's second law of motion:
Force = mass × acceleration.
The mass of the passenger is given as 52 kg, and the acceleration of the elevator is given as 1.2 m/s^2. Substituting these values into the formula, we get:
Force due to acceleration = 52 kg × 1.2 m/s^2.
Next, let's calculate the force due to gravity. The force due to gravity is given by multiplying the mass of the passenger by the acceleration due to gravity, which is 9.8 m/s^2:
Force due to gravity = 52 kg × 9.8 m/s^2.
Now, we can find the total upward force exerted by the floor of the elevator on the passenger by adding the two forces together:
Total upward force = Force due to acceleration + Force due to gravity.
Substituting the calculated values, we have:
Total upward force = (52 kg × 1.2 m/s^2) + (52 kg × 9.8 m/s^2).
Multiplying each term, we get:
Total upward force = 62.4 N + 509.6 N.
Adding the two forces together, we find:
Total upward force = 572 N.
Therefore, the upward force exerted by the floor of the elevator on the 52 kg passenger is 572 Newtons (N).