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:
An object’s weight is proportional to its mass.
Answer:
The magnitude of force must you apply to hold the platform in this position = 888.89 N
Explanation:
Given that :
Workdone (W) = 80.0 J
length x = 0.180 m
The equation for this work done by the spring is expressed as:

Making the spring constant
the subject of the formula; we have:

Substituting our given values, we have:


The magnitude of the force that must be apply to the hold platform in this position is given by the formula :


F = 888.89 N
Answer:
μ = 0.0315
Explanation:
Since the car moves on a horizontal surface, if we sum forces equal to zero on the Y-axis, we can determine the value of the normal force exerted by the ground on the vehicle. This force is equal to the weight of the cart (product of its mass by gravity)
N = m*g (1)
The friction force is equal to the product of the normal force by the coefficient of friction.
F = μ*N (2)
This way replacing 1 in 2, we have:
F = μ*m*g (2)
Using the theorem of work and energy, which tells us that the sum of the potential and kinetic energies and the work done on a body is equal to the final kinetic energy of the body. We can determine an equation that relates the frictional force to the initial speed of the carriage, so we will determine the coefficient of friction.

where:
vf = final velocity = 0
vi = initial velocity = 85 [km/h] = 23.61 [m/s]
d = displacement = 900 [m]
F = friction force [N]
The final velocity is zero since when the vehicle has traveled 900 meters its velocity is zero.
Now replacing:
(1/2)*m*(23.61)^2 = μ*m*g*d
0.5*(23.61)^2 = μ*9,81*900
μ = 0.0315
Answer:
D
The answer cannot be found until it is known whether q is greater than, less than, or equal to 45°.
Explanation:
Since block moves with constant speed
So, frictional force
f = FCosq
Work done by friction
W = - fd
W = - fd Cos q
The answer may be greater or less than - fdSinq. It depends on the value of q which is less than, or equal to 45°.