What will a spring scale read for the weight of a 75-kg woman in an elevator that moves upward with acceleration of 0.30-g?
Unsure of how to solve this problem. Can someone please walk me through it step by step. Thank you
W=mg+ma =m(g+a) =
=m(g+0.3g)= 1.3mg
To solve this problem step-by-step, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
Step 1: Convert the woman's weight from kilograms to newtons.
The weight of an object is given by the equation W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity. In this case, the woman's weight can be calculated as W = (75 kg) * (9.8 m/s^2) = 735 N.
Step 2: Calculate the net force acting on the woman.
The net force can be calculated using the equation F_net = ma, where F_net is the net force, m is the mass, and a is the acceleration. In this case, the acceleration is given as 0.30g, and we need to convert it to m/s^2. Since 1 g = 9.8 m/s^2, we have a = (0.30)(9.8 m/s^2) = 2.94 m/s^2.
Step 3: Substitute the values into the equation.
We can substitute the calculated values into the equation F_net = ma as follows: F_net = (75 kg)(2.94 m/s^2) = 220.5 N.
Step 4: Determine the tension in the spring scale.
Since the elevator is moving upward, the spring scale will read the apparent weight of the woman, which is equal to the net force acting on her. Therefore, the spring scale will read a weight of 220.5 N.
In summary, the spring scale will read a weight of 220.5 N for a 75-kg woman in an elevator that moves upward with an acceleration of 0.30-g.
To determine the reading on a spring scale for the weight of a person in an elevator, we need to consider the forces acting on the person. In this case, we have the force of gravity pulling the person downward and the upward force exerted by the elevator due to its acceleration.
Let's start by calculating the force of gravity acting on the woman. The force of gravity can be calculated using the equation:
F_gravity = m * g
Where:
F_gravity is the force of gravity
m is the mass (75 kg)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
Substituting in the given values, we have:
F_gravity = 75 kg * 9.8 m/s^2
F_gravity ā 735 N
Now, let's calculate the force exerted by the elevator due to its acceleration. The force exerted by the elevator can be calculated using the equation:
F_elevator = m * a
Where:
F_elevator is the force exerted by the elevator
m is the mass (75 kg)
a is the acceleration of the elevator (0.30 * g)
Substituting in the given values, we have:
F_elevator = 75 kg * (0.3 * 9.8 m/s^2)
F_elevator ā 220.5 N
Since the elevator is moving upward, the force exerted by the elevator will be in the same direction as the force of gravity. Therefore, the net force acting on the woman will be the sum of the force of gravity and the force exerted by the elevator:
Net force = F_gravity + F_elevator
Net force = 735 N + 220.5 N
Net force ā 955.5 N
Finally, the reading on the spring scale will be equal to the net force acting on the woman, which is approximately 955.5 Newtons. Therefore, the spring scale will read approximately 955.5 N.