# A spring with a constant of #1 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #2 kg# and speed of #3 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

The compression is

The spring constant is

The kinetic energy of the object is

This kinetic energy will be stored in the spring as potential energy.

So,

By signing up, you agree to our Terms of Service and Privacy Policy

To find the compression of the spring, we can use the conservation of mechanical energy principle. The initial kinetic energy of the object is equal to the potential energy stored in the spring when it comes to rest.

The initial kinetic energy of the object is given by:

( KE_{initial} = \frac{1}{2}mv^2 ) ( KE_{initial} = \frac{1}{2}(2 , \text{kg})(3 , \text{m/s})^2 ) ( KE_{initial} = 9 , \text{J} )

The potential energy stored in the spring when it is compressed is given by:

( PE_{spring} = \frac{1}{2}kx^2 ) ( PE_{spring} = \frac{1}{2}(1 , \text{kg/s}^2)(x)^2 ) ( PE_{spring} = \frac{1}{2}(1 , \text{kg/s}^2)(x)^2 )

Setting the initial kinetic energy equal to the potential energy of the spring when compressed:

( KE_{initial} = PE_{spring} ) ( 9 , \text{J} = \frac{1}{2}(1 , \text{kg/s}^2)(x)^2 )

Solving for ( x ):

( 9 = \frac{1}{2}x^2 ) ( 18 = x^2 ) ( x = \sqrt{18} ) ( x = 3\sqrt{2} )

Therefore, the spring will compress by ( 3\sqrt{2} ) meters.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A spring with a constant of #8 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #8 kg# and speed of #6 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
- If a rocket with a mass of 4000 tons vertically accelerates at a rate of # 12/5 m/s^2#, how much power will the rocket have to exert to maintain its acceleration at 11 seconds?
- A force of 30 newtons is applied to a machin e through a distance of 10 meters. The machine is designed to lift an objec t to a height of 2 meters. If the total work output for the machine is 18 newton-meters (N-m), what is the techanical advantage of the machine?
- A spring with a constant of #7 (kg)/(s^2)# is lying on the ground with one end attached to a wall. An object with a mass of #4 kg # and speed of # 7 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
- An object with a mass of #300 kg# is hanging from an axle with a radius of #3 cm#. If the wheel attached to the axle has a radius of #120 cm#, how much work would it take to turn the wheel a length equal to the circumference of the axle?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7