
Concept explainers
(a)
The time of the jump and acceleration during the time.

Answer to Problem 91QAP
The time of the jump is
Explanation of Solution
Givendata:
Distance, for take-off speed
Distance for acceleration necessary to attain the required speed from rest
Final speed
Initial speed
Formula Used:
Newton's second law:
Calculation:
We are interested in the portionof the jump while the insect is still on the ground.
We can assume that the acceleration of theinsect is constant during this phase
In order to calculate the acceleration of the insect and thelength of time during this phase of the jump, we first need to calculate the speed with whichthe froghopper leaves the ground.
While the insect is in the air, it is only under the influenceof gravity, so we can use the constant acceleration equations and the height of the jump tocalculate the takeoff speed.
Once we have this value, we know the froghopper acceleratedfrom rest through a distance of
The forces acting on the insectwhile it is on the ground are the force of the ground on the froghopper pointing up (that is,the normal force) and the force of gravity pointing down.
After defining a coordinate systemwhere positive y points upward, we can calculate the magnitude of the normal force usingNewton's second law.
Takeoff speed is,
Acceleration necessary to attain that speed from rest is,
Time is,
Conclusion:
The time of the froghopper jump is
(b)
The free body diagram of the grasshopper during the leap.

Explanation of Solution
Free body diagram of the grasshopper during the leap is,
Where,
(c)
The force that ground exert on the froghopper during the jump in millinewtons and represent it as a multiple of insect's weight.

Answer to Problem 91QAP
The force that ground exert on the froghopper during the jump in millinewtons is
And the force
Explanation of Solution
Given data:
Distance, for take-off speed
Distance for acceleration necessary to attain the required speed from rest
Final speed
Initial speed
Formula Used:
Newton's second law:
Calculation:
We are interested in the portionof the jump while the insect is still on the ground.
We can assume that the acceleration of the insect is constant during this phase
In order to calculate the acceleration of the insect and the length of time during this phase of the jump. We first need to calculate the speed with which the froghopper leaves the ground.
While the insect is in the air, it is only under the influence of gravity, so we can use the constant acceleration equations and the height of the jump to calculate the takeoff speed.
Once we have this value, we know the froghopper accelerated from rest through a distance of
We can directly calculate the time because we are assuming the acceleration is constant.
The forces acting on the insect while it is on the ground are the force of the ground on the froghopper pointing up (that is, the normal force) and the force of gravity pointing down.
After defining a coordinate system where positive y points upward, we can calculate the magnitude of the normal force using Newton's second law.
froghopper's weight
This force is
Conclusion:
Thus, we have the value of force
And the force is
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Chapter 4 Solutions
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