m = mass = 5 kg
= initial velocity = 100 m/s
= final velocity = ?
I = impulse = 30 Ns
Using the impulse-change in momentum equation
I = m( -
)
30 = 5 ( - 100)
= 106 m/s
The drawing shows an object attached to an ideal spring, which is hanging from the ceiling. The unstrained length of the spring
is indicated. For purposes of measuring the height h that determines the gravitational potential energy, the floor is taken as the position where h = 0 m. The equilibrium position at which the object hangs stationary is identified as position 2. The object is set into vertical simple harmonic motion between positions 1 and 3. Identify the positions where the kinetic energy KE, the elastic potential energy EPE, and the gravitational potential energy GPE each have their maximum values during an oscillation cycle.
1 answer:
Image is missing so I have attached it.
Also, the options are missing and it is;
A) KE is has a maximum value at position 3. EPE has a maximum value at position 2. GPE has a maximum value at position 1.
B) KE is has a maximum value at position 1. EPE has a maximum value at position 2. GPE has a maximum value at position 3.
C) KE is has a maximum value at position 2. EPE has a maximum value at position 3. GPE has a maximum value at position 1.
D) KE is has a maximum value at position 1. EPE has a maximum value at position 3. GPE has a maximum value at position 2.
E) KE is has a maximum value at position 2. EPE has a maximum value at position 1. GPE has a maximum value at position 3.
Answer:
Option C is the correct answer which says; KE is has a maximum value at position 2. EPE has a maximum value at position 3. GPE has a maximum value at position 1.
Explanation:
If an object vibrates about its mean position, under the influence of a restoring force, such that restoring force is directly proportional to the displacement from the mean position, the motion of the object is called simple harmonic motion. During Simple harmonic motion, the sum of Kinetic and potential energy remains constant.
Now, Looking at the diagram, Kinetic Energy (KE) is maximum at position 2.
Looking at the options, only C and E agree with this.
Thus, our answer is either option C or E.
However, Option E is not going to be right because it says that GPE is at a maximum at position 3, which is not true as the maximum GPE will occur at position 1.
Thus,
Option C fulfills that and therefore will be the correct answer.
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1) The kinetic energy of an object is given by:
where m is the object's mass and v its speed.
By using this equation, we find the initial kinetic energy of the skateboarder:
and the final kinetic energy as well:
So, her change in kinetic energy is
2) The work-energy theorem states that the work done to increase the speed of an object is equal to the variation of kinetic energy of the object:
Therefore, the work done by the skateboarder is
where m is the object's mass and v its speed.
By using this equation, we find the initial kinetic energy of the skateboarder:
and the final kinetic energy as well:
So, her change in kinetic energy is
2) The work-energy theorem states that the work done to increase the speed of an object is equal to the variation of kinetic energy of the object:
Therefore, the work done by the skateboarder is
Answer:
a = 5.05 x 10¹⁴ m/s²
Explanation:
Consider the motion along the horizontal direction
= velocity along the horizontal direction = 3.0 x 10⁶ m/s
t = time of travel
X = horizontal distance traveled = 11 cm = 0.11 m
Time of travel can be given as
inserting the values
t = 0.11/(3.0 x 10⁶)
t = 3.67 x 10⁻⁸ sec
Consider the motion along the vertical direction
Y = vertical distance traveled = 34 cm = 0.34 m
a = acceleration = ?
t = time of travel = 3.67 x 10⁻⁸ sec
= initial velocity along the vertical direction = 0 m/s
Using the kinematics equation
Y = t + (0.5) a t²
0.34 = (0) (3.67 x 10⁻⁸) + (0.5) a (3.67 x 10⁻⁸)²
a = 5.05 x 10¹⁴ m/s²
Answer:
The resulting, needed force for equilibrium is a reaction from a support, located at 2.57 meters from the heavy end. It is vertical, possitive (upwards) and 700 N.
Explanation:
This is a horizontal bar.
For transitional equilibrium, we just need a force opposed to its weight, thus vertical and possitive (ascendent). Its magnitude is the sum of the two weights, 400+300 = 700 N, since weight, as gravity is vertical and negative.
Now, the tricky part is the point of application, which involves rotational equilibrium. But this is quite simple if we write down an equation for dynamic momentum with respect to the heavy end (not the light end where the additional weight is placed). The condition is that the sum of momenta with respect to this (any) point of the solid bar is zero:
Where momenta from weights are possitive and the opposed force creates an oppossed momentum, then a negative term. Solving our unknown d:
So, the resulting force is a reaction from a support, located at 2.57 meters from the heavy end (the one opposed to the added weight end).
