An object is projected straight upward with an initial speed of 25.0 m/s
1 answer:
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Answer:
a) λ = 1.12 m
b) f = 5.41 Hz
c) v = 154.54 m/s
d) A = 0.22m
e)
Explanation:
You have the following equation for a wave traveling on a cord:
(1)
The general expression for a wave is given by:
(2)
By comparing the equation (1) and (2) you have:
A: amplitude of the wave = 0.22m
k: wave number = 5.6 m^-1
w: angular velocity = 34 rad/s
a) The wavelength is given by substitution in the following expression:
b) The frequency is:
c) The velocity of the wave is:
d) The amplitude is 0.22m
e) To calculate the maximum and minimum speed of the particles you obtain the derivative of the equation of the wave, in time:
cos function has a minimum value -1 and maximum +1. Then, you obtain for maximum and minimum velocity:
Answer:
a) u_s=0.375
b )v=14.4 m/s
Explanation:
1 Concepts and Principles
Particle in Equilibrium: If a particle maintains a constant velocity (so that a = 0), which could include a velocity of zero, the forces on the particle balance and Newton's second law reduces to:
∑F=0 (1)
2- Particle in Uniform Circular Motion:
If a particle moves in a circle or a circular arc of radius Rat constant speed v, the particle is said to be in uniform circular motion. It then experiences a net centripetal force F and a centripetal acceleration a_c. The magnitude of this force is:
F=ma_c
=m*v^2/R (2)
where m is the mass of the particle F and a_c are directed toward the center of curvature of the particle's path.
<em>3- The magnitude of the static frictional force between a static object and a surface is given by:</em>
f_s=u_s*n (3)
where u_s is the coefficient of kinetic friction between the object and the surface and n is the magnitude of the normal force.
Given Data
R (radius of the car's path) = 170 m
v (speed of the car) = 25 m/s
Required Data
- In part (a), we are asked to find the coefficient of static friction u_s that will prevent the car from sliding.
- In part (b), we are asked to find the speed of the car v if the coefficient of static friction is one-third u_s found in part (a).
Solution:
see the attachment pic
Since the car is not accelerating vertically, we can model it as a particle in equilibrium in the vertical direction and apply Equation (1)
∑F_y=n-mg
= mg (4)
We model the car as a particle in uniform circular motion in the horizontal direction. The force that enables the car to remain in its circular path is the force of static friction at the point of contact between road and tires. Apply Equation (2) to the horizontal direction:
∑F_x=f_s
=m*v^2/R
Substitute for f_s from Equation (3):
u_s=m*v^2/R
Substitute for n from Equation (4):
u_s*mg=m*v^2/R
u_s*g = v^2/R
Solve for u_s:
u_s= v^2/Rg (5)
Substitute numerical values:
u_s=0.375
(b)
The new coefficient of static friction between the tires and the pavement is:
u_s'=u_s/3
Substitute u_s/3 for u_s in Equation (5):
u_s/3=v^2/Rg
Solve for v:
v=14.4 m/s
Answer:
μ = 0.498
Explanation:
I manage to find the picture of this problem. In the attached picture you can also see the forces involved in this case.
We know according to newton's law that the static friction force is:
Fs = μ * N
However, as you can see in the picture, the Normal force is equals to the weight, in this case the weight of the painter and also the ladder, therefore:
N = Fy
and the force of the friction is:
Fs = Fx
Therefore the coefficient is:
μ = Fx/Fy (1)
Now, let's write the equations in x and y, to solve this.
For the "x" axis:
Fx - Fw = 0 -----> Fx = Fw (2)
Fw is force of the wall, while Fx is the force friction in the x axis (base of the ladder).
for the "y" axis:
Fy - W1 - W2 = 0
W1 = mg (ladder)
W2 = Mg (painter)
replacing we have:
Fy = W1 + W2
Fy = mg + Mg ----> Fy = g(m + M) (3)
To get the force that the wall is exerting we need to calculate the torque around the foot of the ladder so:
τ = rF sinθ
However, the angle in the wall and the ladder is 90° so:
τ = rF sin90°
τ = rF (4)
replacing (4) with the forces we have:
rFw = rW1 + rW2
4Fw = 1.5mg + 2.1Mg
Fw = 1.5mg + 2.1Mg/4 (5)
Finally, with this expression, we can replace it in (1) to get the coefficient of friction:
μ = Fx/Fy
μ = 1.5mg + 2.1Mg / 4g(m + M) gravity cancels out so:
μ = 1.5m + 2.1M / 4(m + M)
Replacing the data we finally have:
μ = (1.5 * 2) + (2.1 * 55) / 4 (55 + 12)
μ = 133.5 / 268
<h2>μ = 0.498</h2>