Answer :
The correct answer is that the dumpster will exert a torque of approximately 2280 N·m on the lever.
To calculate the torque exerted by the dumpster on the lever, we use the formula for torque, which is given by:
[tex]\[ \tau = r \times F \][/tex]
where:
- [tex]\( \tau \)[/tex] is the torque in newton-meters [tex](N·m),[/tex]
- [tex]\( r \)[/tex] is the distance from the pivot to the point where the force is applied in meters (m),
- [tex]\( F \)[/tex] is the force in newtons (N).
Given that the force exerted by the dumpster due to its weight is 5700 N and the distance from the pivot to the point where the force is applied is 0.40 m, we can plug these values into the formula to find the torque:
[tex]\[ \tau = 0.40 \, \text{m} \times 5700 \, \text{N} \][/tex]
[tex]\[ \tau = 2280 \, \text{N·m} \][/tex]
Therefore, the dumpster will exert a torque of 2280 N·m on the lever. This is the amount of rotational force that needs to be overcome by an equal and opposite torque to lift the dumpster using the lever."
Final answer:
The amount of torque exerted by the dumpster on the lever can be calculated using the formula: torque = force x distance. Given the force of 5700 N and the distance of 0.40 m, the resulting torque is 2280 N·m.
Explanation:
In this physics problem, we're dealing with the concept of torque, which is a measure of the force that can cause an object to rotate about a pivot. The amount of torque depends on two things: the amount of force applied and the distance at which the force is applied from the pivot point. This is calculated using the formula: torque = force x distance.
If a dumpster exerts a downward force of 5700 N (its weight) at a distance of 0.40 m from the lever's pivot, the amount of torque can be calculated as follows:
Torque = Force x Distance
Torque = 5700 N x 0.40 m
Torque = 2280 N·m
Therefore, the dumpster will exert a torque of 2280 N·m on the lever.
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