The period of a pendulum is the time it takes the pendulum to swing back and forth once. If the only dimensional quantities that
1 answer:
Clarification:
Let T signify the pendulum's period. The time's SI unit is seconds (s).
It is influenced by the length of the pendulum, l, and the gravitational acceleration, g.
The SI units for gravitational acceleration, g, and pendulum length, l, are m/s² and m, respectively.
Dividing m by m/s² produces s². Taking the square root of s² results in s, which is the SI unit for the pendulum's period.
Thus,
This concludes the solution we sought.
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a) The student's speed after jumping is 1.07 m/s
b) The final speed of the laser is 10.4 m/s
Explanation:
a)
This issue can be approached through the momentum conservation principle: In the absence of external forces, the combined momentum of the student and the laser must remain unchanged. Hence, we can express:
where:
The initial momentum is zero
m = 42 kg signifies the mass of the laser
v = 1.5 m/s is the laser's final velocity
M = 59 kg is the mass of the student
V denotes the student's final velocity
Solving this for V, we can determine the student's speed:
Thus, the student's final speed calculates to 1.07 m/s.
b)
Here, both the laser and the student have a combined speed of 3.1 m/s prior to the student's jump; thus, the initial momentum isn't zero.
<pSo, we formulate the equation of momentum conservation as:where:
m = 42 kg denotes the mass of the laser
M = 59 kg is the student’s mass
u = 3.1 m/s is their starting velocity
V = -2.1 m/s indicates the student's speed post-jump (she jumps backward)
v signifies the laser's final speed
When we resolve for v, we have:
Learn more about momentum:
To start, we first need to determine the kinetic energy of the penny before it strikes the ground. This is calculated using the formula where m equals 5.25 g, which is 0.00525 kg for the penny's mass, and v equals 3.27 m/s for its speed. Replacing the values into the equation provides: When the penny lands, all this kinetic energy transforms into internal energy for both the penny and the ground. If half of this energy goes into the penny's internal energy, the change is determined by a specific formula where m is the penny's mass, Cs is its specific heat capacity (2.03 J/gC), and 
, the change in temperature. To find the last element, the equation will be solved.