The figure shows the velocity graph of a 79kg passenger in an elevator.
The graph is (0,0),(1,4),(5,8),(9,2)
What is the passenger's apparent weight at t=1s,5s,9s?
To determine the passenger's apparent weight at t=1s, 5s, and 9s, we need to consider the relationship between velocity and apparent weight.
The apparent weight of an object can be calculated using the following equation:
Apparent weight = True weight - Net force
When the velocity is positive (going upwards), the net force is greater than the force of gravity, and the apparent weight is greater than the true weight. When the velocity is negative (going downwards), the net force is less than the force of gravity, and the apparent weight is less than the true weight.
Let's calculate the apparent weight at t=1s, 5s, and 9s using the given velocity graph.
At t=1s:
The velocity is 4 m/s, which is positive, indicating that the elevator is moving upwards. Therefore, the apparent weight will be greater than the true weight.
At t=5s:
The velocity is 8 m/s, which is positive, indicating that the elevator is still moving upwards. Therefore, the apparent weight will be greater than the true weight.
At t=9s:
The velocity is 2 m/s, which is positive, indicating that the elevator is still moving upwards. Therefore, the apparent weight will be greater than the true weight.
Please note that without the specific values for the true weight and the forces involved, we can only determine the relationship between the velocity and the apparent weight but cannot calculate the actual values for the apparent weight.
To determine the passenger's apparent weight at different times, we need to analyze the graph of their velocity. The apparent weight of the passenger in an elevator can be calculated using the formula:
Apparent Weight = Weight + Mass * Acceleration
Given that the mass of the passenger is 79 kg, we also need the acceleration. We can find the acceleration from the velocity graph by calculating the change in velocity divided by the change in time, which gives us the average rate of change of velocity over a given time interval.
Let's calculate the acceleration at different time intervals using the given velocity graph:
At t=1s:
- Velocity at t=0s is 0 m/s.
- Velocity at t=1s is 4 m/s.
Change in velocity = Final velocity - Initial velocity
= 4 m/s - 0 m/s
= 4 m/s
Change in time = 1s - 0s = 1s
Acceleration = Change in velocity / Change in time
= 4 m/s / 1s
= 4 m/s^2
Now we can calculate the apparent weight at t=1s:
Apparent Weight = Weight + Mass * Acceleration
Given that the weight is equal to the mass multiplied by the acceleration due to gravity (9.8 m/s^2), we can calculate the apparent weight as:
Apparent Weight = 79 kg * 9.8 m/s^2 + 79 kg * 4 m/s^2
= 771.2 N + 316 N
= 1087.2 N (rounded to one decimal place)
Therefore, the passenger's apparent weight at t=1s is approximately 1087.2 N.
Similarly, you can calculate the apparent weight at t=5s and t=9s using the same approach.