6.1 Work and Energy

6.1 Work and Energy

Multiple Choice

What is energy?

• It is a form of heat

• It is the capacity to burn coal

• It is the ability to do work or to produce transformations

• It is a property of the matter used to meassure forces

Open Ended

What is work?

Gravitational Potential Energy

• Is the energy of an object due to its position above the surface of the Earth

• When work is done to lift an object up at a constant speed it gains gravitational potential energy

•  $\Delta E_p=W=\overrightarrow{F}\Delta\overrightarrow{d}$  

 $E_p=mgh$  

• Ep = gravitational potential energy (J)

• m = mass (kg)

• g = acceleration due to gravity ( $\frac{m}{s^2}$  )

• h = height above reference (m)

• A reference point is an arbitrarily chosen point where the potential energy is set to zero

Multiple Choice

How could you increase the gravitational potential energy of an object without changing its mass and gravity?

• Make the object larger

• Lower the object towards the ground

• Raise the object farther off the ground

• Allow the object to roll on the ground

Multiple Choice

What is the gravitational potential energy of a 26 kg eagle, flying at an altitude of 65 m at a speed of 19 m/s?

• 32,110 J

• 1690 J

• 172.4 J

• 16,562 J

Multiple Choice

The highest inhabited town in the world has an elevation of 5.334 km above sea level. What would be the gravitational potential energy of a 64.0 kg person in this town?

• 3.35x10³ J

• 3.41x10⁵ J

• 3.35x10⁶ J

• 3.348x10⁹ J

Kinetic Energy

• Energy due to the motion of an object

•  $E_k=\frac{1}{2}mv^2$  

• Ek = kinetic energy

• m= mass (kg)

• v = speed (m/s)

Multiple Choice

A pitcher throws a 148 g baseball, giving it a kinetic energy of 134 J. Determine the speed of the ball

• 1.35 m/s

• 42.6 m/s

• 21.3 m/s

• 1.81 m/s

Hooke's Law

• The defamation of an object is directly proportional to the force causing it

•  $\overrightarrow{F_s}=-k\overrightarrow{x}$  

• The meaning of the negative sign is that the direction of the restoring force is always opposite to the direction of the displacement

• The spring constant (k) is number that indicates the stiffness of the spring

Multiple Choice

Which of the following springs is the stiffest?

• A spring that requires a froce of 2000 N to compress it by 6.8 m.

• A spring that requires a force of 4000 N to stretch it by 9.0 m.

• A spring that requires a force of 8000 N to compress it by 45 m.

• A spring that requires a force of 4800 N to stretch it by 14 m.

Multiple Choice

What force should be applied to compress a spring by 0.013 m if its spring constant is k = 1900 N/m?

• 1880 N

• 24.7 N

• 1900 N

• 0.127 N

For a vertical spring, a larger mass is required to compress the spring further from the equilibrium position (x=0)

Multiple Choice

A spring has a spring constant of 330 N/m. How far is the spring compressed if 150 N of force are used?

• 2.2 m

• 0.0014 m

• 5.0 m

• 0.45 m

Multiple Choice

A mass of 0.64 kg extends a spring by 0.42 m. Calculate the spring constant.

• 14.93 Nm^-1

• 0.27 Nm^-1

• 1.52 Nm^-1

• 2.7 Nm^-1

Multiple Choice

Hooke's Law fails when a material reaches its:

• breakdown

• elastic limit

• end of tether

• fracture stress

Elastic Potential Energy

• The amount of energy stored in a spring is equal to the work done on it

• For force vs. displacement graphs, work is the area under the line

•  $E_p=\frac{1}{2}kx^2$  

Multiple Choice

Calculate the elastic potential energy Leo puts into the trampoline mat when he stretches the mat (k= 473 Nm^-1) by 0.35 m.

• 2.887 J

• 28.97 J

• 82.775 J

• 12.76. J

Multiple Choice

Ben has a mass of 37 kg and is stretching the trampoline mat by 0.30 m. Calculate the elastic potential energy he stores in the mat.

• 54.39 J

• 246.67 J

• 3.87 J

• 83 J

Multiple Choice

Leo (70 Kg) stretches the trampoline mat by 37 cm. Calculate the elastic potential energy he puts into the trampoline mat.

• 4.79 J

• 126.9 J

• 47.9 J

• 12.76. J