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6) True: the car is exerting an equal and opposite force on the truck
7) True: the astronaut can drift back by throwing the tool forward
8) True: the bug exerts an equal and opposite force on you
9) Second Law
Explanation:
6)
This problem can be solved by applying Newton's third law of motion, which states that:
"When an object A exerts a force (action) on another object B, then object B exerts an equal and opposite force (reaction) on object A"
In this problem, we can identify the car and the truck as object A and object B. Here we are told that the truck is exerting a force on the car: therefore, according to Newton's third law, the car is also exerting an equal and opposite force on the truck.
Therefore, the statement is true.
7)
This problem can be also solved by thinking in terms of the Newton's third law of motion.
In fact, at the beginning the astronaut is drifting away from the space station. When he throws away the tool, in the forward direction (away from the space station), he exerts a force on the tool: we can identify this force as the action force, and its direction is away from the space station.
As a result, according to Newton's third law, the tool will also exert a reaction force (equal and opposite) on the astronaut: therefore, the force exerted by the tool on the astronaut is toward the space station, and therefore the astronaut will be pushed back towards the station.
Therefore, the statement is true.
8)
Again, this problem can also be explained using Newton's third law.
In fact, the moment you step on the bug, your foot exerts a force (the action force) on the bug, pushing downward.
As a result, according to Newton's third law, the bug exerts back on you an equal and opposite force (upward). The reason you don't feel this force at all is that your mass is much larger than that of the bug, therefore your acceleration is negligible.
Therefore, the statement is true.
9)
This problem can be explained by using Newton's second law, which states that the net force acting on an object is equal to the product between its mass and its acceleration. Mathematically:
where
F is the net force
m is the mass
a is the acceleration
In this problem, the ball slows down as it crosses the field: this means that it has an acceleration (more precisely, a negative acceleration). According to the law, this means also that there is a net, unbalanced force acting on it, in the direction opposite to the motion of the ball. In fact, this force is the force of friction between the ball and the surface.
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Work needed: 720 J
Explanation:
The work needed to stretch a spring is equal to the elastic potential energy stored in the spring when it is stretched, which is given by
where
k is the spring constant
x is the stretching of the spring from the equilibrium position
In this problem, we have
E = 90 J (work done to stretch the spring)
x = 0.2 m (stretching)
Therefore, the spring constant is
Now we can find what is the work done to stretch the spring by an additional 0.4 m, that means to a total displacement of
x = 0.2 + 0.4 = 0.6 m
Substituting,
Therefore, the additional work needed is
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Explanation:
We have,
Semimajor axis is
It is required to find the orbital period of a dwarf planet. Let T is time period. The relation between the time period and the semi major axis is given by Kepler's third law. Its mathematical form is given by :
G is universal gravitational constant
M is solar mass
Plugging all the values,
Since,
So, the orbital period of a dwarf planet is 138.52 years.