Solve Spring Problem: 97.6g Ball Dropped from 58.7cm

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In summary, a 97.6 g ball was dropped from a height of 58.7 cm above a spring of negligible mass. The ball compressed the spring to a maximum displacement of 4.60282 cm. After converting to meters and using the equations mgh and .5k(deltax)^2, the spring constant was determined to be 530 N/m. It was later realized that the incorrect value for h was used, leading to the wrong answer.
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lzh
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Homework Statement


A(n) 97.6 g ball is dropped from a height of
58.7 cm above a spring of negligible mass.
The ball compresses the spring to a maximum
displacement of 4.60282 cm.
The acceleration of gravity is 9.8 m/s2 :


Homework Equations


mgh
.5k(deltax)^2


The Attempt at a Solution


I first converted all grams to kg, and cm to m:
97.6g=.0976kg
58.7cm=.587m
4.60282cm=.0460282m
then:
mgh=.5k(deltax)^2
(.0976g)(9.8m/s^2)(.587m)=.5k(.0460282m)^2
k=530N/m

I really don't see what i could've done wrong, but this isn't the right answer, according to my homework service
 
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  • #2
Hint: you took the wrong h.
 
  • #3
lol, i forgot to add deltax to h
 

FAQ: Solve Spring Problem: 97.6g Ball Dropped from 58.7cm

How do you calculate the potential energy of the ball?

The potential energy of the ball can be calculated using the formula PE = mgh, where m is the mass of the ball (97.6g), g is the gravitational acceleration (9.8 m/s^2), and h is the height from which the ball is dropped (58.7cm or 0.587m). Plugging in these values, we get PE = (0.0976kg)(9.8 m/s^2)(0.587m) = 0.565 J.

What is the equation for the kinetic energy of the ball?

The equation for kinetic energy is KE = 1/2mv^2, where m is the mass of the ball (97.6g) and v is the velocity of the ball when it hits the spring. Since the ball is dropped from a height and has no initial velocity, v can be calculated using the equation v = √(2gh), where g is the gravitational acceleration (9.8 m/s^2) and h is the height (0.587m). Plugging in these values, we get v = √(2)(9.8 m/s^2)(0.587m) = 3.84 m/s. Thus, the kinetic energy of the ball is KE = 1/2(0.0976kg)(3.84 m/s)^2 = 0.711 J.

How do you determine the spring constant of the spring?

The spring constant, k, can be determined using the equation k = F/x, where F is the force exerted on the spring and x is the displacement of the spring. In this problem, the force exerted on the spring is equal to the weight of the ball, which is calculated as mg = (0.0976kg)(9.8 m/s^2) = 0.957 N. The displacement of the spring can be calculated using the equation x = h - d, where h is the initial height of the ball (0.587m) and d is the maximum compression of the spring (unknown in this problem). Therefore, the spring constant can be found by rearranging the equation to k = F/(h-d).

How do you find the maximum compression of the spring?

The maximum compression of the spring can be found by equating the potential energy of the ball at its initial height to the potential energy of the spring at its maximum compression. This can be represented as PE(ball) = PE(spring), which can be expanded to mgh = 1/2kx^2. Plugging in the values calculated in the previous questions, we get (0.0976kg)(9.8 m/s^2)(0.587m) = 1/2kx^2. Rearranging the equation to solve for x, we get x = √(2mgh/k) = √((2)(0.0976kg)(9.8 m/s^2)(0.587m)/(k)). Therefore, the maximum compression of the spring can be calculated once the spring constant is known.

What is the final velocity of the ball after it bounces off the spring?

Assuming no energy is lost during the collision, the final velocity of the ball after it bounces off the spring can be calculated using the conservation of energy principle. This means that the kinetic energy of the ball after the collision will be equal to the potential energy it had before hitting the spring. Using the equation KE = 1/2mv^2, we can solve for v and get v = √(2PE/m) = √(2(0.565 J)/(0.0976kg)) = 3.84 m/s. This is the same velocity calculated in question 2, since the energy of the ball is conserved.

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