Q: For the same system, what is the maximum force $$F_{max}$$ that can be applied to $$m_2 so $$that $$m_1$$ does not slip off $$m_2$$?

$$F_{max} = \mu_k m_1$ g \left(1 + \frac{m_2$}{m_1$}\right) = 0.4 \times 1 \times 9.8 \times (1 + 2/1) = 11.76\ \mathrm{N}$$

Q: A mass $$m is $$attached to a string and swings in a horizontal circle of radius $$R$$, making a constant angle $$\theta$$ with the vertical. What is the angular frequency $$\omega$$?

$$\omega = \sqrt{\frac{g \tan \theta}{R}}$$

Question 1

A 1 kg block (m₁) rests on top of a 2 kg block (m₂) as shown. The coefficient of kinetic friction between the blocks is $$\mu_k = 0.4. $$The floor is frictionless. If a horizontal force $$F = 20\ \mathrm{N} is $$applied to $$m_2$$, what is the acceleration of $$m_2$$?

Accepted Answer

$$a = \frac{F - f_{k}}{m_1$ + m_2$}$$ where $$f_{k} = \mu_k m_1$ g$$, so $$a = \frac{20 - (0.4)(1)(9.8)}{3} = 5.69\ \mathrm{m/s^2$}$$

Question 2

For the same system, what is the maximum force $$F_{max}$$ that can be applied to $$m_2 so $$that $$m_1$$ does not slip off $$m_2$$?

Accepted Answer

$$F_{max} = \mu_k m_1$ g \left(1 + \frac{m_2$}{m_1$}ight) = 0.4 	imes 1 	imes 9.8 	imes (1 + 2/1) = 11.76\ \mathrm{N}$$

Question 3

A 500 N person stands on a 250 N platform and pulls on a rope attached to a frictionless pulley system (see image). What force must the person exert to move the platform upward at a steady rate?

Accepted Answer

$$F = 375\ \mathrm{N}$$

Question 4

A 500 N person stands on a 250 N platform. Another person on the ground pulls the rope attached to the same frictionless pulley system. What force must the person on the ground exert to move the platform upward at a steady rate?

Accepted Answer

$$F = 625\ \mathrm{N}$$

Question 5

Three blocks are in contact on a frictionless surface and pushed by a force $$F as $$shown. How does the normal force $$n_{1\ on\ 2} ($$block 1 on 2) compare to $$n_{2\ on\ 3} ($$block 2 on 3)?

Accepted Answer

$$n_{1\ on\ 2} = n_{2\ on\ 3}$$

Question 6

A ladybug sits at the outer edge of a turntable, and a gentleman bug sits halfway between her and the axis. The turntable starts rotating ever more rapidly. What is the first event that will occur?

Accepted Answer

The ladybug falls off.

Question 7

If the turntable is at rest and the ladybug and gentleman bug are on opposite edges, but the gentleman bug is much more massive, who will fall off first as the turntable speeds up?

Accepted Answer

The ladybug

Question 8

A mass $$m is $$attached to a string and swings in a horizontal circle of radius $$R$$, making a constant angle $$	heta$$ with the vertical. What is the angular frequency $$\omega$$?

Accepted Answer

$$\omega = \sqrt{\frac{g 	an 	heta}{R}}$$

Question 9

Which of the following is NOT a fundamental force in nature?

Accepted Answer

Frictional

Question 10

Which of the following is NOT a state of matter?

Accepted Answer

Crystal

Question 11

Which of the following is NOT a framework of physical law?

Accepted Answer

Thermodynamic

Question 12

Which of the following is NOT a system model used in physics?

Accepted Answer

Molecule

Question 13

A block of mass $$m$$ slides on a frictionless surface and collides elastically with a stationary block of mass $$2m. $$What is the velocity of the first block after the collision?

Accepted Answer

$$v_1$$' = \frac{m - 2m}{m + 2m} $$v_1$$ = -\frac{1}{3} $$v_1$$

Question 14

A block of mass $$m is $$attached to a spring with spring constant $$k$$ and oscillates on a frictionless surface. What is the period of oscillation?

Accepted Answer

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

Question 15

A car of mass $$m$$ moves at speed $$v$$ around a flat circular track of radius $$R. $$What is the minimum coefficient of friction $$\mu$$ required to prevent slipping?

Accepted Answer

$$\mu = \frac{v^2$}{gR}$$

Question 16

A block slides down a frictionless incline of height $$h. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 17

A force $$F is $$applied to a block of mass $$m on a $$horizontal frictionless surface. What is the acceleration of the block?

Accepted Answer

$$a = \frac{F}{m}$$

Forces, Friction, and Acceleration in a Two-Block System

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