Answer:
L = 0.99 m = 99 cm
Explanation:
The period is the reciprocal of the frequency.
T = 1/0.5 = 2.0 s
T = 2π√(L/g)
L = g(T/2π)²
L = 9.8(2.0/2π)² = 0.99 m
If the system accelerates upward, it will cause the apparent gravity to increase. This will require a longer pendulum to keep the same period, or shorten the period if the length remains the same. This shows up in the equation where the product of gravity and the square of the period must remain constant for the length to remain constant.
F = 2820.1 N
Explanation:
Let the (+)x-axis be up along the slope. The component of the weight of the crate along the slope is -mgsin15° (pointing down the slope). The force that keeps the crate from sliding is F. Therefore, we can write Newton's 2nd law along the x-axis as
Fnet = ma = 0 (a = 0 no sliding)
= F - mgsin15°
= 0
or
F = mgsin15°
= (120 kg)(9.8 m/s^2)sin15°
= 2820.1 N
Answer:
(c) 16 m/s²
Explanation:
The position is ![r(t) = [3.0 \text{ m} - (4.00 \text{ m/s})t]\hat{i} + [6.0 \text{m} - (8.00 \text{ m/s}^2 )t^2 ]\hat{j}](https://tex.z-dn.net/?f=r%28t%29%20%3D%20%5B3.0%20%5Ctext%7B%20m%7D%20-%20%284.00%20%5Ctext%7B%20m%2Fs%7D%29t%5D%5Chat%7Bi%7D%20%2B%20%5B6.0%20%5Ctext%7Bm%7D%20-%20%288.00%20%5Ctext%7B%20m%2Fs%7D%5E2%20%29t%5E2%20%5D%5Chat%7Bj%7D)
.
The velocity is the first time-derivative of <em>r(t).</em>
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The acceleration is the first time-derivative of the velocity.
Since <em>a(t)</em> does not have the variable <em>t</em>, it is constant. Hence, at any time,
Its magnitude is 16 m/s².
Answer:
the units of work and energy is joule and unit of power is Watt
