1.)a mass of 180 g is held by a horizontal spring of spring constant 22N/m. it i
ID: 2239453 • Letter: 1
Question
1.)a mass of 180 g is held by a horizontal spring of spring constant 22N/m. it is displaced from its equilibrium position and released from rest. As it passes through its equilibrium position, its speed is 5.8 m/s. (a) for the motion from the release position to the equilibrium position, what is the work done by the spring? b.) what was the magnitude of the initial displacement? [i got the answer to number one is, 3.0J, but i don't know how to get the displacement.] 2.) A pendulum consists of a mass hanging from a string of length 1.0 m attached to the ceiling. Suppose that this pendulum is initially held at an angle of 30 degrees with the vertical and then released. a.) what is the speed with which the mass swings through its lowest point? b.) For the same initial angle, at what angle with the vertical will the mass have one half of this speed? [i answered to part a and the velocity is 1.6m/s but i can't get the right degrees for part b.] 3.) you are to design a roller coaster in which cars start from rest at a height h=33.0 m, roll down into a valley and then up a mountain. Neglect friction. a.) what is the speed of the cars at the bottom of the valley? b.) if the passengers are to feel 9.0g at the bottom of the valley, what must be the radius R of the arc of the circle that fits the bottom of the valley? c.) The top of the next mountain is an arc of a circle of the same radius R. If the passengers are to feel 0g at the top of this mountain, what must be its height, h? [i got the answer to part a, which is 25.4 m/s. i also got the answer to part b, which is 7.31 m. i just can't get the answer to c]Explanation / Answer
1)
At the equilibrium position its speed is 5.8m/s.
Its kinetic energy is then 0.5 mv^2 = 0.5 *0.18*5.8^2 =3.027 J
Its potential energy is zero.
Total energy is 3.027 J,
At the initial positon its potential energy was 0.5*kx^2 ant its k.e was zero.
Total energy at that position is 3.027 = 0.5*kx^2 = 0.5*22 *x^2
Hence initial displacement x = 0.524m.
2)
v1 = k sin ? =k sin 30 = k /2.
v2 = v1/2 =k /4 =k sin ?
sin ?= 0.25
? = 14.48?
3)
c)
This combines energy and forces.. First, we need to know how fast the ride should be going for 0g's.. That uses forces. Then we can calculate h using energy.
The forces are....
W = -mg
N = 0 (0 g's, remember?)
N + W = m * ac
0 - mg = m v
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.