Physics Plez Help !!!?

Question

1. A certain dam is holding back fresh water 209 m deep. What is the water pressure at the base of the dam?

2.}
A 0.90 kg mass attached to a vertical spring of force constant 139 N/m oscillates with a maximum speed of 0.33 m/s. Find the following quantities related to the motion of the mass.
(a) the period
(b) the amplitude
(c) the maximum magnitude of the acceleration


3.}A bunch of grapes is placed in a spring scale at a supermarket. The grapes oscillate up and down with a period of 0.37 s, and the spring in the scale has a force constant of 670 N/m.

(a) What is the mass of the grapes?
(b) What is the weight of the grapes?

Answer 1

1. A certain dam is holding back fresh water 209 m deep. What is the water pressure at the base of the dam?
2.09x10^5 kg/m^2 or 2.05x10^6 N/m^2

2. A 0.90 kg mass attached to a vertical spring of force constant 139 N/m oscillates with a maximum speed of 0.33 m/s. Find the following quantities related to the motion of the mass.
(a) the period
First let us calculate sqrt(K/M) = sqrt((139kg/s^2)/(0.90kg)) = 12.4/s
Hence the period is: 2*pi/sqrt(K/M) = 2*3.14159/12.4s = 0.51s
(b) the amplitude
First write the wave function as: x = A*sin( sqrt(K/M)*t)
velocity as: dx/dt = A*sqrt(K/M)*cos( sqrt(K/M)*t) ....(1)
Given: A*sqrt(K/M) = 0.33 m/s,
we have the amplitude A = 0.33/12.4 = 0.027 (m).
(c) the maximum magnitude of the acceleration
From (1): d2x/dt2 = -A*(K/M)*sin( sqrt(K/M)*t), and thus the maximum magnitude of the acceleration is: 0.33*12.4 = 4.1 (m/s^2)

3.}A bunch of grapes is placed in a spring scale at a supermarket. The grapes oscillate up and down with a period of 0.37 s, and the spring in the scale has a force constant of 670 N/m.
(a) What is the mass of the grapes?
(b) What is the weight of the grapes?
we need to use the formula: f = (1/2*pi)*sqrt(K/M), or:
2*3.14159/0.37 = sqrt(K/M)
M = 670/(2*3.14159/0.37)^2 = 2.3 (kg)
W = 9.8*M = 23 N