Start with the conservation of energy. The spring potential energy and the mass' kinetic energy will fluctuate over time, but their sum will stay constant. The maximum spring potential energy equals the maximum kinetic energy.
0.5mv² = 0.5kx²
m is the mass, v is the maximum velocity, k is the spring constant, and x is the maximum displacement along the spring.
Given values:
m = 4.1kg
v = 0.78m/s
Calculate the maximum kinetic energy.
Max KE = 0.5mv² = 1.247J
Set this equal to the maximum spring potential energy.
Max spring PE = 0.5kx² = 1.247J
<em>x² = 2.494/k</em>
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The spring force is F = kx
Max F = kx = 13N
x = 13/k
<em>x² = 169/k²</em>
Set both values of x² equal to each other and solve for k the spring constant:
2.494/k = 169/k²
2.494k = 169
k = 67.8N/m
Use k to find x:
Max F = kx = 13N
67.8x = 13
x = 0.192m
The frequency of the system is given by:
f = (1/(2π))√(k/m)
f is the frequency, k is the spring constant, m is the mass.
f = (1/(2π))√(67.8/4.1)
f = 0.647Hz
Answer:
the unit of work is derived unit because joule is defined the work done by the force aftab 1 newton causing the displacement of one metre something newton metre(n-m) is also used to measuring work.
The mass attached to the spring must be 0.72 kg
Explanation:
The frequency of vibration of a spring-mass system is given by:
(1)
where
k is the spring constant
m is the mass attached to the spring
We can find the spring constant by using Hookes' law:
where
F is the force applied on the spring
x is the stretching of the spring
When a mass of m = 2.82 kg is applied to the spring, the force applied is the weight of the mass, so we have
and using 
and 
, we find
Now we want the frequency of vibration to be
f = 7.42 Hz
So we can rearrange eq.(1) to find the mass m that we need to attach to the spring:
#LearnwithBrainly
Answer:
Explanation:
This problem can be solved with the conservation of the momentum.
If the ball is fired upward, the momentum before and after the ball is fired must conserve. Hence, the speed of the ball is the same that the speed of the car just in the moment in wich the ball is fired.
Hence, the result depends of the acceleration of the car. If the change in the speed is higher than the speed of the ball, it is probably that the ball will be behind the car or it will come back to the car.
If the ball is fired forward, and if the change in the speed of the car is not enogh, the ball will be in front of the car.
HOPE THIS HELPS!!
