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Increasing the angle of inclination of the plane decreases the velocity of the block as it leaves the spring.
- The statement that indicates how the relationship between <em>v</em> and <em>x</em> changes is;<u> As </u><u><em>x</em></u><u> increases, </u><u><em>v</em></u><u> increases, but the relationship is no longer linear and the values of </u><u><em>v</em></u><u> will be less for the same value of </u><u><em>x</em></u><u>.</u>
Reasons:
The energy given to the block by the spring =
According to the principle of conservation of energy, we have;
On a flat plane, energy given to the block = = kinetic energy of
block =
Therefore;
0.5·k·x² = 0.5·m·v²
Which gives;
x² ∝ v²
x ∝ v
On a plane inclined at an angle θ, we have;
The energy of the spring =
- The force of the weight of the block on the string,
The energy given to the block = = The kinetic energy of block as it leaves the spring =
Which gives;
Which is of the form;
a·x² - b = c·v²
a·x² + c·v² = b
Where;
a, b, and <em>c</em> are constants
The graph of the equation a·x² + c·v² = b is an ellipse
Therefore;
- As <em>x</em> increases, <em>v</em> increases, however, the value of <em>v</em> obtained will be lesser than the same value of <em>x</em> as when the block is on a flat plane.
<em>Please find attached a drawing related to the question obtained from a similar question online</em>
<em>The possible question options are;</em>
- <em>As x increases, v increases, but the relationship is no longer linear and the values of v will be less for the same value of x</em>
- <em>The relationship is no longer linear and v will be more for the same value of x</em>
- <em>The relationship is still linear, with lesser value of v</em>
- <em>The relationship is still linear, with higher value of v</em>
- <em>The relationship is still linear, but vary inversely, such that as x increases, v decreases</em>
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1. • Here, force of gravity on the block = 20 N.
• Therefore, the normal force will also be the same, i.e., 20 N [According to Newton's Third Law, on every action, there is an equal and opposite reaction]
• The coefficient
• Force of friction =
• Hence, the force of sliding friction between the block and the ground is 8 N.
• So, it is option c. 8 N
2. The answer is option d. continue in the same direction with no change in speed.
We know, force = mass × acceleration. When force is 0, then acceleration will also be 0 since mass cannot be 0. So, there will be no change in speed.
3. It is option b. force that is required to give a one kilogram object the acceleration of 1 m/s^2.
Newton is the SI unit of force. As mentioned earlier, force = mass × acceleration. The SI unit of mass and acceleration is Kg and m/s^2 respectively.
So, 1 N = 1 Kg × 1 m/s^2.
4. It is d. not zero.
Acceleration is the change in speed. So, if the force is zero, then acceleration will not occur.
5. Force = 2 N
Acceleration of the object A = 2 m/s^2.
Acceleration of the object B = 1 m/s^2.
Therefore, mass of the object A = 2 N ÷ 2 m/s^2 = 1 Kg
And, mass of the object B = 2 N ÷ 1 m/s^2 = 2 Kg
So, the mass of object B is greater than that of object A.
Hence, the answer is option c. Object B has more mass.
Hope you could get an idea from here.
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