Q: A door is $$1 m $$wide. If a $$10 N $$force is applied perpendicular to the door at the edge farthest from the hinge, what is the torque about the hinge?

$$10\ \mathrm{N} \times 1\ \mathrm{m} = 10\ \mathrm{N \cdot m}$$

Question 1

A uniform meter stick is supported at the 25-cm mark in equilibrium when a 1-kg rock is suspended at the 0-cm end. The mass of the meter stick is:

Accepted Answer

equal to the mass of the rock

Question 2

A force $$F$$ moves an object along the $$x-$$axis in the same direction as the force. The graph shows the force as a function of the object's position. What is the work done by the force when the object moves from $$0.0 to$$ $$4.0 m$$?

Accepted Answer

$$60\ \mathrm{J}$$

Question 3

Three forces, each with the same magnitude, are exerted on a door as shown. $$F_1$$ acts at the middle of the door, and the other two act at the end of the door. If counterclockwise torques (calculated about the hinge) are considered positive, which of the following statements correctly orders the torques exerted by the three forces?

Accepted Answer

torque 3 \u003c torque 2 \u003c torque 1

Question 4

An injured skier is pulled up a ski mountain on a medical sled at constant speed. Consider the injured skier and sled as a single object. Which of the following forces do negative work on the injured skier and sled in this process?

Accepted Answer

Gravity, kinetic friction between sled and snow, and air drag on the sled

Question 5

Which of the following accurately describe properties of conservative forces? (Select ALL that apply.)

Accepted Answer

Net work done by these forces between any two points is independent of the path taken

Question 6

The position of a particular simple harmonic oscillator as a function of time is given by $$x(t) = A \cos(\omega t)$$, where $$A = 20\ \mathrm{cm}$$ and $$\omega = 0.5\ \mathrm{rad/s}. $$What is the period of oscillation?

Accepted Answer

$$T = \frac{2\pi}{\omega} = 12.57\ \mathrm{s}$$

Question 7

For the oscillator $$x(t) = A \cos(\omega t)$$, with $$A = 20\ \mathrm{cm}$$ and $$\omega = 0.5\ \mathrm{rad/s}$$, what is the maximum velocity?

Accepted Answer

$$v_{max} = A \omega = 10\ \mathrm{cm/s}$$

Question 8

For the oscillator $$x(t) = A \cos(\omega t)$$, with $$A = 20\ \mathrm{cm}$$ and $$\omega = 0.5\ \mathrm{rad/s}$$, what is the maximum acceleration?

Accepted Answer

$$a_{max} = A \$$omega^2$$ = 5\ \mathrm{cm/s^2$}$$

Question 9

At $$t = 0 sec$$, what is the acceleration of the oscillator $$x(t) = A \cos(\omega t)$$?

Accepted Answer

$$a(0) = -A \$$omega^2$$

Question 10

At $$t = 0 sec$$, what is the velocity of the oscillator $$x(t) = A \cos(\omega t)$$?

Accepted Answer

$$v(0) = 0$$

Question 11

Which of the following is true for torque $$	au$$, which for a given force $$\vec{F}$$ and a lever arm of length $$r$$, is given by $$	au = F r \sin 	heta$$? (Select ALL that apply.)

Accepted Answer

An object with a non-zero net torque on it must have a non-zero angular acceleration.

Question 12

Astronauts in space determine their mass by oscillating on a large spring. If the period of oscillation is $$3\ \mathrm{s}$$, what is the angular frequency?

Accepted Answer

$$\omega = \frac{2\pi}{3}\ \mathrm{rad/s}$$

Question 13

Suppose an astronaut oscillates on a spring with a period $$T. If $$the spring constant is $$k$$ and the astronaut's mass is $$m$$, which equation relates these quantities?

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}}$$

Question 14

A force $$F$$ acts on an object, moving it from $$x=0 to$$ $$x=4 m. $$The force is $$10 N $$from $$x=0 to$$ $$x=2 m$$, and $$20 N $$from $$x=2 to$$ $$x=4 m. $$What is the total work done?

Accepted Answer

$$60\ \mathrm{J}$$

Question 15

A door is $$1 m $$wide. If a $$10 N $$force is applied perpendicular to the door at the edge farthest from the hinge, what is the torque about the hinge?

Accepted Answer

$$10\ \mathrm{N} 	imes 1\ \mathrm{m} = 10\ \mathrm{N \cdot m}$$

Question 16

A skier is pulled up a slope at constant speed. Which force does positive work on the skier?

Accepted Answer

Tension in the rope

Question 17

Which of the following is NOT a property of conservative forces?

Accepted Answer

Work done depends on the path taken

Question 18

A simple harmonic oscillator has $$x(t) = A \cos(\omega t). At $$what time $$t is $$the velocity maximum?

Accepted Answer

$$t = \frac{\pi}{2\omega}$$

Physics Study Notes: Forces, Work, Torque, and Oscillations

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