# Spring constant, find height of projectile

• subopolois
In summary, the problem involves a 48 gram dart being shot vertically upwards from a catapult with a spring constant of 350 N/m. The catapult is initially stretched from the equilibrium point by 21 cm. To find the height above the starting point reached by the dart, the formula h = v^2/2g can be used. Taking into account the increase in gravitational potential energy of the dart, the formula v = d√(k/m) can be used to calculate the speed at which the dart leaves the catapult. However, there is a better approach where energy conservation can be used to find the height without calculating the speed.
subopolois

## Homework Statement

A 48 gram dart is shot vertically upwards from a catapult with a spring constant of 350 N/m. The catapult is initially stretched from the equilibrium point by 21 cm. What is the height above the starting point reached by the dart?

## Homework Equations

KE=PE, rearranging to find h gets h= v^2/2g

find the velocity as it leaves the catapult as v= d(sqrt(k/m))

## The Attempt at a Solution

v= 0.21m (sqrt(350Nm/0.048kg))
= 17.93 m/s

h= (17.93m/s)^2 / 2(9.81m/s^2)
= 16.38 m

does this seem right?

When you calculated the speed at which the dart leaves the catapult, did you take into account the increase in gravitational potential energy of the dart? How did you get the formula v = d√(k/m)?

I did not, how would i do that?
I did take gravity into account when i found the height...

You could find the speed at which the dart leaves the catapult by using conservation of energy. You will need to include kinetic energy, gravitational potential energy, and elastic potential energy.

There is a better approach to the problem. You don't need to find the speed at which the dart leaves the catapult. Is energy conserved overall between the point of release and the point where the dart reaches the highest point?

## 1. What is the formula for finding the spring constant?

The formula for finding the spring constant is k = F/x, where k is the spring constant, F is the force applied, and x is the displacement of the spring.

## 2. How do you calculate the height of a projectile using the spring constant?

The height of a projectile can be calculated using the formula h = (k/m) * v^2, where h is the height, k is the spring constant, m is the mass of the object, and v is the velocity of the object.

## 3. Can the spring constant change over time?

Yes, the spring constant can change over time if the material or temperature of the spring changes. However, for most practical purposes, the spring constant can be assumed to remain constant.

## 4. What factors affect the spring constant?

The spring constant is affected by the material and shape of the spring, as well as the temperature and any external forces applied to the spring.

## 5. How is the spring constant measured in experiments?

The spring constant can be measured experimentally by applying known forces to the spring and measuring the displacement of the spring. The slope of the force-displacement graph will give the value of the spring constant.

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