Question 1

A bobsled starts from rest at the end of the launching section and attempts to make it through a vertical loop. Neglecting air resistance and friction, which principle best explains why the bobsled cannot make it through the loop if it starts from rest at the end of the launching section?

Accepted Answer

The bobsled lacks sufficient gravitational potential energy to convert into the required kinetic energy at the top of the loop.

Question 2

At the top of a vertical loop, the minimum speed $$v_{top}$$ required for a bobsled to remain in contact with the track is determined by the balance of forces. Which equation correctly expresses this condition?

Accepted Answer

$$\frac{mv_{top}^2}{R} = mg$$

Question 3

A bobsled of mass $$m$$ starts from a height $$h$$ above the ground and enters a loop of radius $$R. $$Neglecting friction and air resistance, what is the minimum height $$h_{min}$$ required for the bobsled to just make it through the loop?

Accepted Answer

$$h_{min} = \frac{5}{2}R$$

Question 4

If friction is present and the coefficient of kinetic friction between the bobsled and the track is $$\mu_k$$, what is the minimum distance $$D$$ required for the bobsled to stop after the loop, starting from an initial energy $$E_{i}$$?

Accepted Answer

$$D = \frac{E_{i}}{\mu_k mg}$$

Question 5

A bobsled is pushed with a force $$F_{push}$$ over a distance $$L$$ and then enters a loop of radius $$R. If $$the work done by the push and gravity is $$3mgR$$, what is the exit velocity $$v_{f} of $$the bobsled?

Accepted Answer

$$v_{f} = \sqrt{3gR}$$

Question 6

If air resistance causes the bobsled to exit the loop with only 80% of its theoretical speed, what fraction of the initial kinetic energy is lost to air resistance?

Accepted Answer

$$\frac{9}{25}$$

Question 7

Two cars of equal mass $$m$$ collide inelastically at an intersection. Car 1 moves east at $$v_1$$, and car 2 moves north at $$v_2. $$What is the magnitude of the velocity $$v_f of $$the combined mass after the collision?

Accepted Answer

$$v_f = \sqrt{v_1$^2 + v_2$^2}$$

Question 8

A yo-yo consists of two disks of mass $$M$$ and radius $$R$$ connected by a central cylinder of negligible mass and radius $$R/2. $$What is the rotational inertia $$I_{tot} of $$the yo-yo about its axis of symmetry?

Accepted Answer

$$I_{tot} = \frac{3}{2}MR^2$

Question 9

For the yo-yo described above, if the tension in the string is $$T$$ and the acceleration of the center of mass is $$a$$, which equation correctly relates $$T$$ and $$a$$?

Accepted Answer

$$T = \frac{4Mg}{3}$$

Question 10

A yo-yo of mass $$M is $$released from rest and drops a height $$h. $$What is its speed $$v at $$the bottom, assuming no energy is lost to friction?

Accepted Answer

$$v = \sqrt{3gh}$$

Question 11

In a collision between two cars of equal mass $$m$$, one moving east at $$v$$ and the other north at $$v$$, what is the direction of the velocity of the combined mass after the collision?

Accepted Answer

45 degrees north of east

Question 12

A bobsled of mass $$m$$ starts from rest at a height $$h$$ and enters a loop of radius $$R. If $$the coefficient of friction is $$\mu_k$$, what is the work done by friction as the bobsled travels a distance $$D$$?

Accepted Answer

$$W_{fric} = \mu_k mg D$$

Question 13

A yo-yo is released from rest and falls vertically. If the string is wound around the central cylinder of radius $$R/2$$, what is the angular acceleration $$\alpha of $$the yo-yo?

Accepted Answer

$$\alpha = \frac{3g}{2R}$$

Question 14

In the context of a bobsled loop, which of the following best describes the role of the normal force at the top of the loop?

Accepted Answer

It is zero when the bobsled is just about to lose contact with the track.

Question 15

A bobsled of mass $$m is $$pushed with a force $$F$$ over a distance $$L$$ before entering a loop. What is the total work done on the bobsled before the loop?

Accepted Answer

$$W = F \cdot L$$

Question 16

If a bobsled loses energy due to air resistance while traversing a loop, how is the work done by air resistance related to the change in kinetic energy?

Accepted Answer

It is equal in magnitude to the decrease in kinetic energy.

Question 17

A yo-yo of mass $$M$$ and radius $$R is $$released from rest and falls a distance $$h. If $$the rotational inertia is $$I_{tot} = \frac{3}{2}MR^2$, what is the final velocity v$ at the bottom?

Accepted Answer

$$v = \sqrt{3gh}$$

Question 18

In a perfectly inelastic collision between two cars of equal mass $$m$$, one moving east at $$v$$ and the other north at $$v$$, what is the fraction of kinetic energy retained after the collision?

Accepted Answer

$$\frac{1}{2}$$

Physics Study Notes: Conservation of Energy, Circular Motion, Collisions, and Rotational Dynamics

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