Question 1

If it takes 7 N to stretch a spring 8 cm and if the spring is then cut in half,what force does it take to stretch one of the halves 4 cm?​

Accepted Answer

The force required to stretch a spring is directly proportional to the distance it is stretched, according to Hooke's Law. Cutting the spring in half doubles its spring constant but does not change the force needed to stretch it a proportional distance. Therefore, to stretch one half of the spring 4 cm (which is a proportional distance to the original 8 cm stretch), it still requires 7 N.

Question 2

A 0.30-kg object is oscillating on a spring with a spring constant of k = 22.0 N/m.What is the potential energy of the system when the object displacement is 0.035 m,exactly half the maximum amplitude?

Accepted Answer

The potential energy of a spring-mass system is given by the equation:

U = 1/2 k x^2

where k is the spring constant and x is the displacement of the object from its equilibrium position.

At maximum amplitude, the displacement is given by:

A = x_max = F/k

where F is the maximum restoring force of the spring.

Thus, the maximum potential energy of the system is:

U_max = 1/2 k A^2 = 1/2 (22.0 N/m) (0.072 m)^2 = 0.072 J

When the object is at displacement x = 0.035 m, halfway between the equilibrium position and the maximum displacement, the potential energy is given by:

U = 1/2 k x^2 = 1/2 (22.0 N/m) (0.035 m)^2 = 0.013 J

Therefore, the best choice is (C), 0.013 J, as it is the only value that is reasonable and consistent with the physics of the situation.

Question 3

Which is not an example of approximate simple harmonic motion?

Accepted Answer

The bouncing ball does not exhibit simple harmonic motion as it does not move in a periodic motion.

Question 4

Spring #1 has spring constant 61.0 N/m.Spring #2 has an unknown spring constant,but when connected in series with Spring #1,the connected springs have an effective spring constant of 20.0 N/m.What is the spring constant for Spring #2?

Accepted Answer

The formula for springs in series is 1/k_eff = 1/k1 + 1/k2. Solving for k2 with k_eff = 20.0 N/m and k1 = 61.0 N/m gives k2 ≈ 29.8 N/m.

Question 5

Doubling the weight suspended vertically from a coil spring will result in a change in the displacement of the spring's lower end by what factor?

Accepted Answer

According to Hooke's Law, the displacement of a spring is proportional to the force applied to it. Therefore, if we double the weight (force) suspended from the spring, we will double the displacement (distance) the spring stretches. Hence, the ratio of the displacement for the new weight to the displacement for the original weight will be 2:1, or a factor of 2.

Question 6

A mass of 0.40 kg,attached to a spring with a spring constant of 40 N/m,is set into simple harmonic motion.What is the magnitude of the acceleration of the mass when at its maximum displacement of 0.25 m from the equilibrium position?

Accepted Answer

At maximum displacement, the mass is momentarily at rest before starting to move in the opposite direction, therefore, the acceleration is maximum.

Using the equation for simple harmonic motion:

x = A*cos(wt)

where x = displacement, A = amplitude, w = angular frequency

The maximum displacement (A) is 0.25 m.

The angular frequency (w) is given by:

w = sqrt(k/m)

where k = spring constant and m = mass

w = sqrt(40/0.40) = 10 rad/s

At the maximum displacement, the velocity is zero, so the acceleration (a) is given by:

a = -w^2*A

a = -(10)^2*(0.25)

a = -25 m/s^2

Taking the magnitude of the acceleration, we get:

|a| = 25 m/s^2

Therefore, the correct answer is D) 25 m/s^2.

Question 7

A large spring requires a force of 130 N to compress it only 0.01 m.What is the spring constant of the spring?

Accepted Answer

The spring constant (k) is given by the formula:
k = F/x
where F is the force applied and x is the distance by which the spring is compressed.
Substituting the given values:
k = 130 N / 0.01 m = 13 000 N/m
Therefore, the spring constant of the spring is 13 000 N/m, which is option B.

Question 8

A 0.400-kg object is attached to a spring with spring constant k = 10.0 N/m and moves with simple harmonic motion over a horizontal frictionless surface.At the instant that it is displaced from equilibrium by −0.0550 m,what is its acceleration?

Accepted Answer

The equation for the acceleration of an object in simple harmonic motion is given by:

a = -ω²x

where ω is the angular frequency (ω = √(k/m)) and x is the displacement from equilibrium.

Plugging in the given values, we have:

ω = √(k/m) = √(10 N/m / 0.400 kg) = 2.236 Ns/m

x = -0.0550 m

a = -ω²x = -(2.236 Ns/m)² (-0.0550 m) = 1.38 m/s²

Therefore, the answer is D.

Question 9

The SI base units for the spring constant are which of the following?

Accepted Answer

The spring constant (k) has units of force per unit length (N/m), and since 1 N = 1 kg⋅m/s², the units for the spring constant are kg/s².

Question 10

A 0.200-kg object,attached to a spring with spring constant k = 16.0 N/m,is moving on a horizontal frictionless surface in simple harmonic motion of amplitude of 0.0840 m.What is its speed at the instant when its displacement is 0.0420 m? (Hint: Use conservation of energy. )

Accepted Answer

The answer of A 0.200-kg object,attached to a spring with...

Question 11

Three identical springs each have the same spring constant k.If these three springs are attached end to end forming a spring three times the length of one of the original springs,what will be the spring constant of the combination?

Accepted Answer

When springs are connected end to end, they behave as if they are in series. In this case, there are three equal springs in series, so the effective spring constant is given by:

1/keff = 1/k + 1/k + 1/k
1/keff = 3/k

Thus, keff = k/3.

Question 12

A tiny spring,with a spring constant of 1.30 N/m,will be stretched to what displacement by a 0.00500-N force?

Accepted Answer

Hooke's law: F = kxx = F/k = 0.00500 N / 1.30 N/m = 3.85 mm

Question 13

A mass of 0.40 kg,hanging from a spring with a spring constant of 75.0 N/m,is set into an up-and-down simple harmonic motion.What is the speed of the mass when moving through the equilibrium point? The starting displacement from equilibrium is 0.20 m.

Accepted Answer

The speed of the mass at the equilibrium point can be found using the conservation of mechanical energy principle. At the equilibrium point, all the energy is kinetic, and at the starting displacement, all the energy is potential. The potential energy at the starting point is given by $PE = \frac{1}{2}kx^2$, where $k$ is the spring constant and $x$ is the displacement from equilibrium. Substituting the given values, $PE = \frac{1}{2} \times 75.0 \, \text{N/m} \times (0.20 \, \text{m})^2 = 1.5 \, \text{J}$. This potential energy is converted into kinetic energy $KE = \frac{1}{2}mv^2$ at the equilibrium point, where $m$ is the mass and $v$ is the velocity. Solving for $v$, we get $v = \sqrt{\frac{2 \times KE}{m}} = \sqrt{\frac{2 \times 1.5 \, \text{J}}{0.40 \, \text{kg}}} = 2.7 \, \text{m/s}$.

Question 14

A mass of 4.5 kg,resting on a horizontal frictionless surface,is attached on the right to a horizontal spring with spring constant 29 N/m and on the left to a horizontal spring with spring constant 60 N/m.If this system is moved from equilibrium,what is the effective spring constant?

Accepted Answer

The effective spring constant of two springs in parallel is given by:
1/k_eff = 1/k1 + 1/k2
where k1 and k2 are the spring constants of the individual springs. 
Using this formula, we get:
1/k_eff = 1/29 + 1/60
1/k_eff = (60 + 29)/(29*60)
k_eff = 89 N/m (since k_eff > 0, the negative sign in option A and D is incorrect)

Question 15

Two springs,each with spring constant 33.0 N/m,are connected in parallel,and the combination is hung vertically from one end.A 18.0-N weight is then suspended from the other end of the combined spring.How far does the combined spring stretch as it comes to equilibrium?

Accepted Answer

The answer of Two springs,each with spring constant 33.0 N/m,are...

Question 16

A mass of 0.40 kg,hanging from a spring with a spring constant of 82 N/m,is set into an up-and-down simple harmonic motion.What is the speed of the mass when moving through a point at 0.05 m displacement? The starting displacement of the mass is 0.10 m from its equilibrium position.

Accepted Answer

The answer of A mass of 0.40 kg,hanging from a...

Question 17

Tripling the displacement from equilibrium of an object in simple harmonic motion will bring about a change in the magnitude of the object's acceleration by what factor?

Accepted Answer

In simple harmonic motion, acceleration is directly proportional to displacement from equilibrium. Tripling the displacement will triple the acceleration.

Question 18

Two springs,each with spring constant k,are attached end to end in a series fashion.A second pair of identical springs are also attached in series fashion.Then the pair of series attached springs are attached in parallel to each other.What is the effective spring constant of the resulting combination of springs?

Accepted Answer

The answer of Two springs,each with spring constant k,are attached...

Question 19

Suppose there is an object for which F = +kx.What will happen if the object is moved away from equilibrium (x = 0)and released?

Accepted Answer

The force F = +kx indicates a force that increases with displacement in the positive direction, meaning it will accelerate away from equilibrium with increasing acceleration.

Question 20

If a long spring with spring constant k is cut into 4 equal lengths,what is the spring constant of each of the 4 shorter springs?​

Accepted Answer

When a spring is cut into shorter lengths, the spring constant of each piece increases because the spring becomes stiffer. The spring constant, k, is inversely proportional to the length of the spring. Cutting a spring into 4 equal parts makes each part 4 times stiffer, so the spring constant of each shorter spring is 4k.

Quiz 13: Vibrations and Waves

If it takes 7 N to stretch a spring 8 cm and if the spring is then cut in half,what force does it take to stretch one of the halves 4 cm?

A 0.30-kg object is oscillating on a spring with a spring constant of k = 22.0 N/m.What is the potential energy of the system when the object displacement is 0.035 m,exactly half the maximum amplitude?

Which is not an example of approximate simple harmonic motion?

Spring #1 has spring constant 61.0 N/m.Spring #2 has an unknown spring constant,but when connected in series with Spring #1,the connected springs have an effective spring constant of 20.0 N/m.What is the spring constant for Spring #2?

Doubling the weight suspended vertically from a coil spring will result in a change in the displacement of the spring's lower end by what factor?

A mass of 0.40 kg,attached to a spring with a spring constant of 40 N/m,is set into simple harmonic motion.What is the magnitude of the acceleration of the mass when at its maximum displacement of 0.25 m from the equilibrium position?

A large spring requires a force of 130 N to compress it only 0.01 m.What is the spring constant of the spring?

A 0.400-kg object is attached to a spring with spring constant k = 10.0 N/m and moves with simple harmonic motion over a horizontal frictionless surface.At the instant that it is displaced from equilibrium by −0.0550 m,what is its acceleration?

The SI base units for the spring constant are which of the following?

A 0.200-kg object,attached to a spring with spring constant k = 16.0 N/m,is moving on a horizontal frictionless surface in simple harmonic motion of amplitude of 0.0840 m.What is its speed at the instant when its displacement is 0.0420 m? (Hint: Use conservation of energy. )

Three identical springs each have the same spring constant k.If these three springs are attached end to end forming a spring three times the length of one of the original springs,what will be the spring constant of the combination?

A tiny spring,with a spring constant of 1.30 N/m,will be stretched to what displacement by a 0.00500-N force?

A mass of 0.40 kg,hanging from a spring with a spring constant of 75.0 N/m,is set into an up-and-down simple harmonic motion.What is the speed of the mass when moving through the equilibrium point? The starting displacement from equilibrium is 0.20 m.

A mass of 4.5 kg,resting on a horizontal frictionless surface,is attached on the right to a horizontal spring with spring constant 29 N/m and on the left to a horizontal spring with spring constant 60 N/m.If this system is moved from equilibrium,what is the effective spring constant?

Two springs,each with spring constant 33.0 N/m,are connected in parallel,and the combination is hung vertically from one end.A 18.0-N weight is then suspended from the other end of the combined spring.How far does the combined spring stretch as it comes to equilibrium?

A mass of 0.40 kg,hanging from a spring with a spring constant of 82 N/m,is set into an up-and-down simple harmonic motion.What is the speed of the mass when moving through a point at 0.05 m displacement? The starting displacement of the mass is 0.10 m from its equilibrium position.

Tripling the displacement from equilibrium of an object in simple harmonic motion will bring about a change in the magnitude of the object's acceleration by what factor?

Suppose there is an object for which F = +kx.What will happen if the object is moved away from equilibrium (x = 0) and released?

If a long spring with spring constant k is cut into 4 equal lengths,what is the spring constant of each of the 4 shorter springs?

Quiz 13: Vibrations and Waves

If it takes 7 N to stretch a spring 8 cm and if the spring is then cut in half,what force does it take to stretch one of the halves 4 cm?​

A 0.30-kg object is oscillating on a spring with a spring constant of k = 22.0 N/m.What is the potential energy of the system when the object displacement is 0.035 m,exactly half the maximum amplitude?

Which is not an example of approximate simple harmonic motion?

Spring #1 has spring constant 61.0 N/m.Spring #2 has an unknown spring constant,but when connected in series with Spring #1,the connected springs have an effective spring constant of 20.0 N/m.What is the spring constant for Spring #2?

Doubling the weight suspended vertically from a coil spring will result in a change in the displacement of the spring's lower end by what factor?

A mass of 0.40 kg,attached to a spring with a spring constant of 40 N/m,is set into simple harmonic motion.What is the magnitude of the acceleration of the mass when at its maximum displacement of 0.25 m from the equilibrium position?

A large spring requires a force of 130 N to compress it only 0.01 m.What is the spring constant of the spring?

A 0.400-kg object is attached to a spring with spring constant k = 10.0 N/m and moves with simple harmonic motion over a horizontal frictionless surface.At the instant that it is displaced from equilibrium by −0.0550 m,what is its acceleration?

The SI base units for the spring constant are which of the following?

A 0.200-kg object,attached to a spring with spring constant k = 16.0 N/m,is moving on a horizontal frictionless surface in simple harmonic motion of amplitude of 0.0840 m.What is its speed at the instant when its displacement is 0.0420 m? (Hint: Use conservation of energy. )

Three identical springs each have the same spring constant k.If these three springs are attached end to end forming a spring three times the length of one of the original springs,what will be the spring constant of the combination?

A tiny spring,with a spring constant of 1.30 N/m,will be stretched to what displacement by a 0.00500-N force?

A mass of 0.40 kg,hanging from a spring with a spring constant of 75.0 N/m,is set into an up-and-down simple harmonic motion.What is the speed of the mass when moving through the equilibrium point? The starting displacement from equilibrium is 0.20 m.

A mass of 4.5 kg,resting on a horizontal frictionless surface,is attached on the right to a horizontal spring with spring constant 29 N/m and on the left to a horizontal spring with spring constant 60 N/m.If this system is moved from equilibrium,what is the effective spring constant?

Two springs,each with spring constant 33.0 N/m,are connected in parallel,and the combination is hung vertically from one end.A 18.0-N weight is then suspended from the other end of the combined spring.How far does the combined spring stretch as it comes to equilibrium?

A mass of 0.40 kg,hanging from a spring with a spring constant of 82 N/m,is set into an up-and-down simple harmonic motion.What is the speed of the mass when moving through a point at 0.05 m displacement? The starting displacement of the mass is 0.10 m from its equilibrium position.

Tripling the displacement from equilibrium of an object in simple harmonic motion will bring about a change in the magnitude of the object's acceleration by what factor?

Suppose there is an object for which F = +kx.What will happen if the object is moved away from equilibrium (x = 0) and released?

If a long spring with spring constant k is cut into 4 equal lengths,what is the spring constant of each of the 4 shorter springs?​

If it takes 7 N to stretch a spring 8 cm and if the spring is then cut in half,what force does it take to stretch one of the halves 4 cm?

If a long spring with spring constant k is cut into 4 equal lengths,what is the spring constant of each of the 4 shorter springs?