In a mattress test, you drop a 7.0 kg bowling ball from a height of 1.5 m above a mattress, which as a result compresses 15 cm a
s the ball comes to a stop.
(c)How much work does the gravitational force do on the ball while it is compressing the mattress?
(d)How much work does the mattress do on the ball?
(e)Now model the mattress as a single spring with an unknown spring constant k, and consider the whole system formed by the ball, the earth and the mattress. By how much does the potential energy of the mattress increase as it compresses?
(f)What is the value of the spring constant k?
(c)How much work does the gravitational force do on the ball while it is compressing the mattress?
(d)How much work does the mattress do on the ball?
(e)Now model the mattress as a single spring with an unknown spring constant k, and consider the whole system formed by the ball, the earth and the mattress. By how much does the potential energy of the mattress increase as it compresses?
(f)What is the value of the spring constant k?
2 answers:
Answer:
(c) 10.29 J
(d) 113.19 J
(e) 113.19 J
(f) 10061 N/m
Explanation:
15 cm = 0.15 m
Let g = 9.8 m/s2
(c) The work done by gravitational force is the product of gravity force and the distance compressed
(d) By using law of energy conservation with potential energy reference being 0 at the maximum compression point. As the ball falls and come to a stop at the compression point, its potential energy is transferred to elastic energy, which is the work that the mattress does on the ball:
where h = 1.5 + 0.15 = 1.65 m is the vertical distance that it falls.
(e) Before the compression, the potential energy of the mattress is 0. After the compression, the potential energy is 113.19J. So it has increased by 113.19J due to the potential energy transferred from the falling ball.
(f)
You might be interested in
Answer:
A) The resultant force is 43.4 [N]
B) The movement of the heavy crate is going to the right and in the negative direction on the y-axis
Explanation:
We need to make a sketch of the different forces acting on the heavy crate.
In the attached image we can see the forces and the sum of the vector with their respective angles.
Forces in the X-axis
Forces in the y-axis
Using the Pythagorean theorem
The movement of the heavy crate is going to the right and in the negative direction on the y-axis, this can be easily seen in the graphical sum of vectors.
Answer:
d = 1.55 * 10⁻⁶ m
Explanation:
To calculate the distance between the adjacent grooves of the CD, use the formula, ..........(1)
The fringe number, m = 1 since it is a first order maximum
The wavelength of the green laser pointer, = 532 nm = 532 * 10⁻⁹ m
Distance between the central maximum and the first order maximum = 1.1 m
Distance between the screen and the CD = 3 m
= Angle between the incident light and the diffracted light
From the setup shown in the attachment, it is a right angled triangle in which
Putting all appropriate values into equation (1)
