compared to an object that does not roll, but instead slides without friction, should a rolling object be released from the same
1 answer:
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The equation expressing the statement "y varies directly as x" is
Explanation
The statement that varies directly as
is analogous to saying that the ratio of
to
is constant. In other words, when
increases,
likewise increases and that when
decreases,
decreases proportionally.
Mathematically, we express the relationship that the ration of is to
is constant is expressed as;
where
is the constant of proportionality.
We can then solve the relationship for to determine the correct form of the relationship as shown below,
Correct question:
Consider the motion of a 4.00-kg particle that moves with potential energy given by
a) Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m?
b) What is the magnitude of the force on the 4.00-kg particle when it is located at x = 5.00 m?
Answer:
a) 3.33 m/s
b) 0.016 N
Explanation:
a) given:
V = 3.00 m/s
x1 = 1.00 m
x = 5.00
At x = 1.00 m
= 4J
Kinetic energy = (1/2)mv²
= 18J
Total energy will be =
4J + 18J = 22J
At x = 5
= -0.24J
Kinetic energy =
= 2Vf²
Total energy =
2Vf² - 0.024
Using conservation of energy,
Initial total energy = final total energy
22 = 2Vf² - 0.24
Vf² = (22+0.24) / 2
= 3.33 m/s
b) magnitude of force when x = 5.0m
At x = 5.0 m
= 0.016N