Conservational Forces and Potential Energy •Define conservative force, potential energy,

and mechanical energy.

•Explain the potential energy of a spring in terms of its compression when Hooke’s law applies.

•Use the work-energy theorem to show how having only conservative forces leads to

Find speed of wrecking ball if it’s maximum vertical height above target is 10 meters.

PE=mgh and this would equal KE at the target KE= ½ mv2_{. }

### Hooke’s Law

**F=kx **

### Work = W = Fx

### PE=Work

### But doesn’t F change over length of

### spring?

W=Fd W= ½ kx (x) = ½ kx2

## F=kx

## PE = ½ kx

2F=kx if k=2N/m and x=.2m

Two 4.0 kg masses are connected to each other by a spring with a force constant of 25 N/m and a rest length of 1.0 m. If the spring has been compressed to 0.80 m in length and the masses are traveling toward each other at 0.50 m/s (each), what is the total energy in the system?

ME=PE+KE

= ½ kx2 + 2(½ mv2) = 1.5 joules

A spring with a force constant of 5000 N/m and a rest length of 3.0 m is used in a catapult. When compressed to 1.0 m, it is used to launch a 50 kg rock.

However, there is an error in the

release mechanism, so the rock gets launched almost straight up. How high does it go, and how fast is it going

### You are loading a toy dart gun,

### which has two settings, the more

### powerful with the spring

### compressed twice as far as the

### lower setting. If it takes 5.0 J of

Old-fashioned pendulum clocks are powered by masses that need to be wound back to the top of the clock about once a week to counteract

energy lost due to friction and to the chimes. One particular clock has

three masses: 4.0 kg, 4.0 kg, and 6.0 kg. They can drop 1.3 meters. How

A 5.00×105-kg subway train is brought to a stop from a speed of 0.500 m/s in 0.400 m by a large spring bumper at the end of its track. What is the force constant k of the spring?

A pogo stick has a spring with a force

If a spring is stretched a distance of 0.25 m with a force of 20. N, what is the

value of the spring constant?

If the spring constant of a pogo stick is 3500. N/m and the weight of the person on the pogo stick is 700. N, how much is the spring in the bottom of the pogo

A box having a mass of 1.50 kg is

accelerated across a table at 1.50 m/s2. The coefficient of friction on the box is 0.300.

(a) What is the force being applied to
the box? (Use: F_{app} -f_{s }= ma)

(b) If this force were applied by a spring, what would the spring

A spring (k = 2.3 N/m) is attached to an object of mass = 10. kg. If the object is

hung from the ceiling by this spring, how much would the spring be stretched?

If m_{s} = 0.50, how much force must be
applied to a spring (spring constant of

0.80 N/m) which is attached to a block of wood (mass = 4.0 kg) in order to just

### When a 50.0 kg person hangs from a

### 20.0 m bungee cord it stretches to a

### length of 32.0 m.

### (a) Find the spring constant of the

### bungee cord, assuming it obeys

### Hooke's law.

### A spring with a force constant of

### 5.20 N/m has a relaxed length of

If the mass is 10 kg and the spring constant is 25 N/m, how far will the spring compress if a 10 N force is

applied upward. (use Hooke’s law)

What would be the total energy at this point, using the original position as the baseline. (use PE of a spring)

What would be the velocity when the mass returns to the original position if it’s released if we disregard gravity? (use PE of the spring = KE of the mass)

If we add gravity to the calculation will the new speed be less or greater than above?

The staples inside a stapler are kept in place by a spring with a relaxed length of 0.115 m. If the spring constant is 51.0 N/m, how much elastic potential energy is store in the spring when its length is 0.150 m? (use Hooke’s law)

A spring with a force constant of 5.20 N/m has a relaxed length of 2.45 m. When a mass is attached to the end of the spring and allowed to come to rest, the vertical length of the spring is 3.57 m. Calculate the elastic potential energy stored in the spring. (use PE of a spring)

When a 50.0 kg person hangs from a 20.0 m bungee cord it stretches to a length of 32.0 m.

If the mass is 10 kg and the spring constant is 25 N/m, how far will the spring compress if a 10 N force is applied upward.

What would be the total energy at this point, using the original position as the baseline.

What would be the velocity when the mass returns to the original position if it’s released if we disregard gravity? And if we don’t?