How close to the edge of the 24.0 kg table shown in Figure 9-47 can a 60.0 kg person sit without tipping it over?
m
Table is 2.2m long each leg is 5m into the table and there is 1.2m in between each leg. The table is 8m in height.
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To determine how close a person can sit to the edge of the table without tipping it over, we need to consider the balance of torques.
1. First, let's calculate the center of mass of the table. Since the table is symmetrical, the center of mass will be in the middle. The distance from the center of mass to either end of the table is half of its length: 2.2m / 2 = 1.1m.
2. Now, let's determine the torque created by the person sitting at the edge of the table. The torque is calculated by multiplying the weight of the person by the distance between their position and the edge of the table. Torque = weight * distance.
Since the person's weight is 60.0 kg and we want to find the distance, let's substitute the given variables into the equation:
Torque_person = 60.0 kg * distance
3. To keep the table from tipping over, the torque created by the person must be equal to or less than the torque created by the table's weight.
4. The torque created by the table's weight can be calculated by multiplying the weight of the table by the distance from the center of mass to the edge of the table. Torque_table = weight_table * distance_table.
The weight of the table is 24.0 kg * 9.8 m/s^2 (acceleration due to gravity) = 235.2 N. The distance from the center of mass of the table to the edge is 1.1m. So, torque_table = 235.2 N * 1.1m.
5. Setting these two torques equal to each other, we have:
Torque_person = Torque_table
To find the distance from the edge of the table that the person can sit without tipping it over, we can rearrange the equation and solve for distance:
60.0 kg * distance = 235.2 N * 1.1m
6. Now we can solve for distance:
distance = (235.2 N * 1.1m) / 60.0 kg
By calculating the above expression, we find the distance from the edge of the table that a 60.0 kg person can sit without tipping it over.
To determine how close a 60.0 kg person can sit to the edge of the table without tipping it over, we need to consider the moments (torques) acting on the table.
1. First, let's calculate the weight of the table. The weight (W) can be calculated using the formula W = mg, where m is the mass and g is the acceleration due to gravity.
W = 24.0 kg × 9.8 m/s^2
W = 235.2 N
2. The table is supported by two legs, so the weight is distributed evenly among them. Each leg will support half of the weight of the table, so the weight acting on each leg is W/2 = 235.2 N / 2 = 117.6 N.
3. Now, let's calculate the torque caused by the weight of the table. The torque is calculated using the formula Torque = Force × Distance, where Force is the weight acting on each leg and Distance is the distance from the legs to the edge of the table where the person is sitting.
Torque = 117.6 N × Distance
4. To prevent the table from tipping over, the torque caused by the person sitting on the table must be equal and opposite to the torque caused by the weight of the table.
Torque (person) = 60.0 kg × 9.8 m/s^2 × Distance
5. Setting the torques equal to each other, we can solve for the Distance.
117.6 N × Distance = 60.0 kg × 9.8 m/s^2 × Distance
6. Solving for Distance:
Distance = (60.0 kg × 9.8 m/s^2) / 117.6 N
Distance = 5.0 m
Therefore, a 60.0 kg person can sit up to 5.0 m from the edge of the table without tipping it over.