Q: A ball of mass $$0.05 kg is $$compressed against a spring with $$k = 100 N/m by$$ $$0.05 m. $$When released, what is the maximum kinetic energy the ball can have?

$$E_k = \frac{1}{2}k x^2$ = \frac{1}{2} \times 100 \times (0.05)^2$ = 0.125 J$$

Question 1

Which of the following correctly describes the relationship between force and potential energy for a spring with spring constant $$k$$ and displacement $$x$$?

Accepted Answer

$$F_s = -kx$$

Question 2

An object of mass $$m is $$dropped from height $$h. $$What is the expression for its gravitational potential energy relative to the ground?

Accepted Answer

$$U_g = mgh$$

Question 3

A ball of mass $$0.05 kg is $$compressed against a spring with $$k = 100 N/m by$$ $$0.05 m. $$When released, what is the maximum kinetic energy the ball can have?

Accepted Answer

$$E_k = \frac{1}{2}k x^2$ = \frac{1}{2} 	imes 100 	imes (0.05)^2$ = 0.125 J$$

Question 4

On a potential energy graph, at which point is the force on the object zero?

Accepted Answer

Where the slope of the potential energy graph is zero

Question 5

A block of mass $$m is $$attached to a vertical spring of constant $$k$$ and dropped from rest. What is the maximum distance $$D$$ the block will fall before momentarily stopping?

Accepted Answer

$$D = \frac{2mg}{k}$$

Question 6

Which of the following statements about stable equilibrium on a potential energy graph is correct?

Accepted Answer

Stable equilibrium occurs at a minimum of potential energy

Question 7

A 2 kg object slides down a frictionless ramp from a height $$h$$ and comes to rest after traveling $$d = 1.0 m on a $$horizontal surface with coefficient of friction $$\mu = 0.50. $$What is the minimum height $$h$$ required?

Accepted Answer

$$h = \mu d$$

Question 8

For a diatomic molecule, the potential energy as a function of separation $$r$$ has a minimum. What does this minimum represent?

Accepted Answer

The equilibrium bond length where the molecule is most stable

Question 9

If the total energy of a molecule is less than the energy required to break the bond, what is the state of the molecule?

Accepted Answer

Bound state

Question 10

ATP hydrolysis in cells releases energy. What is the main reason energy is released when the O-P bond in ATP is broken?

Accepted Answer

Energy is released because the products are at a lower potential energy than the reactants

Question 11

Which equation correctly relates the force to the slope of the potential energy curve for a one-dimensional system?

Accepted Answer

$$F = -\frac{dU}{dx}$$

Question 12

A ball A of mass $$m$$ moving with speed $$v$$ collides elastically with ball B of mass $$m at $$rest. After the collision, ball A is at rest and ball B moves with speed $$v. $$What is the change in kinetic energy of the system?

Accepted Answer

The total kinetic energy remains the same

Question 13

On a potential energy graph, what does a positive slope indicate about the direction of the force?

Accepted Answer

The force is negative

Question 14

Which of the following best describes the energy required to break a molecular bond?

Accepted Answer

It is equal to the absolute value of the bond's potential energy minimum

Question 15

A spring is stretched by a distance $$D. $$What is the potential energy stored in the spring?

Accepted Answer

$$U_s = \frac{1}{2}kD^2$

Question 16

If the potential energy of a system increases as two objects move apart, what can be said about the force between them?

Accepted Answer

The force is attractive

Question 17

Which of the following is true about the sign of energy change in a system?

Accepted Answer

A positive energy change means energy is gained by the system

Question 18

A potential energy graph has a point where the slope is zero and the graph is concave up. What type of equilibrium is this?

Accepted Answer

Stable equilibrium

Question 19

In the context of molecular bonds, what does the term 'bound state' refer to?

Accepted Answer

A state where the total energy is less than the energy required to break the bond

Practice with Energy: Force, Potential Energy, and Molecular Bonds

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