This figure shows the angular displacement of a pendulum on a planet with five times the earth's gravity. How long is the pendulum's string?1.0 m
3.2 m
0.80 m
4.0 m
Answers
Answer:
Explanation:
It is known that the oscillation period of a pendulum can be described as
,
where T is the oscillation period, L is the length of the pendulum and, g is the gravity.
Solving For the length we get:
.
We know that g equals 5 times earth's gravity,
,
and from the angular displacement graphics, it can be seen that the period is
.
Now, we can easily compute the length of the pendulum:
Explanation:
The period (time per cycle) is 1.0 s. The gravity is 5g or 49 m/s². Therefore:
T = 2π √(L / g)
1.0 s = 2π √(L / 49 m/s²)
L = 1.2 m
Related Questions
Explain the relationship between motion and frame of reference.
(01.01 LC)Two objects of the same mass are in a room. At which of thefollowing distances will the greatest gravitational force be exertedby one object on another?O 2 mO 4 mO 6 mO 8 m
What is the pendulum length whose period is 2.0s ?
The Hubble telescope’s orbit is 5.6 × 105 meters above Earth’s surface. The telescope has a mass of 1.1 × 104 kilograms. Earth exerts a gravitational force of 9.1 × 104 Newtons on the telescope. The magnitude of Earth’s gravitational field strength at this location is
The energy equation, E=12mvx2+12kx2=12kA2, is a useful alternative relationship between velocity and position, especially when energy quantities are also required. If the problem involves a relationship among position, velocity, and acceleration without reference to time, it is usually easier to use the equation for simple harmonic motion, ax=d2xdt2=−kmx (from Newton’s second law) or the energy equation above (from energy conservation) than to use the general expressions for x, vx, and ax as functions of time. Because the energy equation involves x2 and vx2, it cannot tell you the sign of x or of vx; you have to infer the sign from the situation. For instance, if the body is moving from the equilibrium position toward the point of greatest positive displacement, then x is positive and vx is positive.
IDENTIFY the relevant concepts
Energy quantities are required in this problem, therefore it is appropriate to use the energy equation for simple harmonic motion.
SET UP the problem using the following steps
Part A
The following is a list of quantities that describe specific properties of the toy. Identify which of these quantities are known in this problem.
Select all that apply.
Select all that apply.
maximum velocity vmax
amplitude A
force constant k
mass m
total energy E
potential energy U at x
kinetic energy K at x
position x from equilibrium
Part B
What is the kinetic energy of the object on the spring when the spring is compressed 5.1 cm from its equilibrium position?
Part C
What is the potential energy U of the toy when the spring is compressed 5.1 cm from its equilibrium position?
Answers
Answer:
Part A
Mass = 50g
Vmax = 3.2m/s
Amplitude= 6cm
Position x from the equilibrium= 5.1cm
Part B
Kinetic energy = 0.185J
Part C
Potential energy = 0.185J
Explanation:
Kinetic energy = 1/2mv×2
Vmax = wa
w = angular velocity= 53.33rad/s
Kinetic energy = 1/2mv^2×r^2 = 0.185J
Part c
Total energy = 1/2m×Vmax^2= 0.256J
1/2KA^2= 0.256J
K= 142.22N/m (force constant)
Potential energy = 1/2kx^2
=1/2×142.22×0.051^2
= 0.185J
Final answer:
To find the kinetic energy of the toy, we need to use the energy equation for simple harmonic motion and the relationship between velocity and position. We can then substitute the known values to calculate the kinetic energy.
Explanation:
In this problem, we are given the amplitude (A) of the oscillation and the maximum velocity (vmax) achieved by the toy. We need to find the kinetic energy (K) of the toy when the spring is compressed 5.1 cm from its equilibrium position.
To solve for the kinetic energy, we can use the energy equation for simple harmonic motion: K = 1/2mvx2, where m is the mass of the object and vx is the velocity of the object at position x. The mass of the object is given as 50 g, which is equal to 0.05 kg.
Since we know the maximum velocity (vmax = 3.2 m/s), we can use the relationship between velocity and position in simple harmonic motion to find the velocity (vx) at a displacement of 5.1 cm from the equilibrium position. The velocity and position in simple harmonic motion are related by vx = ±ω√(A2 - x2), where ω is the angular frequency of the motion.
Substituting the known values into the equations, we can calculate the kinetic energy of the toy.
Learn more about Simple Harmonic Motion here:
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Answers
Answer:
1.1 x 10⁵m/s²
Explanation:
Given parameters:
Velocity = 452m/s
distance = 0.93m
Unknown:
Acceleration of the bullet = ?
Solution:
To solve this problem, we use one of the kinematics equation which is given below:
V² = U² + 2aS
V is the final velocity
U is the initial velocity = 0m/s
a is the unknown acceleration
S is the distance traveled
So;
452² = 0² + (2 x a x 0.93)
204304 = 1.86a
a = 1.1 x 10⁵m/s²
Final answer:
The acceleration of the bullet in the gun barrel can be calculated using the kinematic equation for motion. By substituying the given values into the equation, we find the acceleration to be approximately 1.095 x 10^5 m/s^2.
Explanation:
The subject of this question is Physics, specifically a topic under mechanics known as kinematics. The problem given can be solved using kinematic equations which are used to describe the motion of an object without considering the forces that cause it to move. In this case, the final velocity (vf) of the bullet is given as 452 m/s, the initial velocity (vi) is assumed to be 0 as it starts from rest, and the distance (d) is given as 0.93 m. We are asked to determine the value of acceleration (a).
Using the kinematic equation vf2 = vi2 + 2ad and substituting the given values, we get (452 m/s)2 = 0 + 2*a*0.93 m. We can rearrange to solve for acceleration to get: a = (452 m/s)2 / (2*0.93 m) = 109523.66 m/s2.
So, the acceleration of the bullet in the gun barrel is approximately 1.095 x 105 m/s2.
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How fast would Keesha say the ball is traveling toward her?
Answers
I notice that even though we're working with frames of reference
here, you never said which frame the '5 km/hr' is measured in.
In fact ! You didn't even say which frame the '12 km/hr' of his
bike is measured in.
So there are several different ways this could go. I'll do it the way
I THINK you meant it, but that doesn't guarantee anything.
-- Simon is riding his bike at 12 km/hr relative to the sidewalk,
away from Keesha.
-- He throws a ball at Keesha, at 5 km/hr relative to his own face.
-- Keesha sees the ball approaching her at (12 - 5) = 7 km/hr
relative to the ground and to her.
Answer:
B
Explanation:
Answers
Answer:
Electrical energy
Explanation:
Electrical energy is the form of energy that results from the existence of an electric current, that is, a flow of electrical charges, through a metallic conductor cable as a result of the potential difference that a generator is applying at its ends.
a. True
b. False
Answers
Answer:True
Explanation:In an ideal situation, equilibrium constants cannot be altered if you change the pressure of a system. However, only change in temperature can result to change in equilibrium constants. If there are the same value of molecules on either side of the equation, then a change of pressure is insignificant to the position of equilibrium.
An equilibrium constant is not changed by a change in pressurea. True
b. False
False! :P
B. Sample A would be best, because the percentage of the energy in an incident wave that remains in a reflected wave from this material is the largest.
C. Sample C would be best, because the percentage of the energy in an incident wave that remains in a reflected wave from this material is the smallest.
D. Sample C would be best, because the percentage of the energy in an incident wave that remains in a reflected wave from this material is the largest.
Answers
Answer: Option C: Sample C would be best, because the percentage of the energy in an incident wave that remains in a reflected wave from this material is the smallest.
Explanation:
The absorption coefficient of the samples is given. Sample A has 30%, Sample B has 47% and Sample C has 62%. This means that sample C absorbs the most percentage of energy incident on it. The energy in the reflected wave would be least. Hence, it would be best to use for a room to make it soundproof.
The correct answer is Option C) Sample C would be best, because the percentage of the energy in an incident wave that remains in a reflected wave from this material is the smallest.
As the coefficient of absorption would define the energy present in the reflected wave, the material C has the highest percentage of absorption i.e. 62% and would be best suitable to make a sound proof room.