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iris [78.8K]
3 years ago
6

the acceleration due to gravity on the moon is 1.6 m/s^2 what is the gravitational potential energy of a 1200 kg lander resting

on top of a 350m hill
Physics
1 answer:
Mumz [18]3 years ago
5 0

<u>Answer</u>

672,000 Joules

<u>Explanation</u>

Gravitational potential energy (P.E) is the energy possessed by a body that is at a potential height from the ground.

IT is calculated by the formula;

P.E = mgh

Where m ⇒ mass

            g ⇒ acceleration due to gravity

            h ⇒ height from trhe ground.

P.E = 1200 × 1.6 × 350

      = 672,000 Joules.

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Answer:

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Explanation:

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\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\\\Rightarrow \frac{1}{-25}-\frac{1}{u}=\frac{1}{\frac{400}{7}}\\\Rightarrow -\frac{1}{u}=\frac{7}{400}+\frac{1}{25}\\\Rightarrow \frac{1}{u}=-\frac{7}{400}-\frac{1}{25}\\\Rightarrow \frac{1}{u}=-0.0575\\\Rightarrow u=-17.4\ cm

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       \alpha = \frac{2*F}{m*r} = \frac{2*34.5N}{35.2kg*0.2m} = 9.8 rad/s2 (4)

  • Since the angular acceleration is constant, we can use the following kinematic equation:

        \omega_{f}^{2}  - \omega_{o}^{2} = 2*\Delta \theta * \alpha (5)

  • Prior to solve it, we need to convert the angle rotated from revs to radians, as follows:

       0.2 rev*\frac{2*\pi rad}{1 rev} = 1.3 rad (6)

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       \omega_{f} = \sqrt{2*\alpha *\Delta\theta} = \sqrt{2*1.3rad*9.8rad/s2} = 5.1 rad/sec (7)

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        v = \omega * r (8)

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       v= 5.1 rad/sec* 0.2 m = 1.01 m/s (9)

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  • There exists a fixed relationship between the tangential and the angular acceleration in a circular movement, as follows:

       a_{t} = \alpha * r (9)

  • where r is the radius of the circular movement. In this case the point is located on the rim of the disk, so r becomes the radius of the disk.
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       a_{t}  = 9.8 rad/s2 * 0.200 m = 1.96 m/s2 (10)

  • Now, the resultant acceleration of a point of the rim, in magnitude, is the vector sum of the tangential acceleration and the radial acceleration.
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       a_{c} = \omega^{2} * r  (11)

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       a_{c} = \omega^{2} * r   = (5.1 rad/sec)^{2} * 0.200 m = 5.2 m/s2 (12)

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