Q: A ball is thrown horizontally from the top of a 45 m high cliff with an initial speed of 10 m/s. Neglecting air resistance, what is the speed of the ball just before it hits the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$\sqrt{10^2$ + (2 \times 9.8 \times 45)} = 31.3\ \mathrm{m/s}$$

Q: A 5 kg box is pressed against a vertical wall. The coefficient of static friction between the box and the wall is $$\mu_s = 0.4. $$What is the minimum horizontal force required to keep the box from sliding down? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

$$F = \frac{mg}{\mu_s} = \frac{5 \times 9.8}{0.4} = 122.5\ \mathrm{N}$$

Q: A 70 kg person stands on a scale in an elevator accelerating upward at $$2\ \mathrm{m/s^2$}. $$What does the scale read?

$$N = m(g + a) = 70 \times (9.8 + 2) = 826\ \mathrm{N}$$

Q: A 0.5 kg block slides on a frictionless track from a height of $$2\ \mathrm{m}$$ and reaches a lower point at $$0.5\ \mathrm{m}. $$What is its speed at the lower point? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2g(h_1$ - h_2$)} = \sqrt{2 \times 9.8 \times (2 - 0.5)} = 5.42\ \mathrm{m/s}$$

Q: A 1 kg object falls from a height of $$10\ \mathrm{m}$$ and hits the ground at $$12\ \mathrm{m/s}. $$How much work was done by air resistance?

$$W_{nc} = \Delta KE + \Delta PE = \frac{1}{2} \times 1 \times 12^2$ - 0 + 0 - 1 \times 9.8 \times 10 = 72 - 98 = -26\ \mathrm{J}$$

Q: A 3 kg object moving at $$6\ \mathrm{m/s}$$ slides to a stop over $$9\ \mathrm{m}$$ due to friction. What is the magnitude of the friction force?

$$f = \frac{\frac{1}{2}mv^2$}{d} = \frac{0.5 \times 3 \times 36}{9} = 6\ \mathrm{N}$$

Q: Two carts, one of mass $$2\ \mathrm{kg}$$ moving at $$3\ \mathrm{m/s}$$ and another of mass $$1\ \mathrm{kg} at $$rest, collide and stick together. What is their final velocity?

$$v_f = \frac{2 \times 3 + 1 \times 0}{2 + 1} = 2\ \mathrm{m/s}$$

Question 1

A ball is thrown horizontally from the top of a 45 m high cliff with an initial speed of 10 m/s. Neglecting air resistance, what is the speed of the ball just before it hits the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\sqrt{10^2$ + (2 	imes 9.8 	imes 45)} = 31.3\ \mathrm{m/s}$$

Question 2

A 5 kg box is pressed against a vertical wall. The coefficient of static friction between the box and the wall is $$\mu_s = 0.4. $$What is the minimum horizontal force required to keep the box from sliding down? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$F = \frac{mg}{\mu_s} = \frac{5 	imes 9.8}{0.4} = 122.5\ \mathrm{N}$$

Question 3

A 70 kg person stands on a scale in an elevator accelerating upward at $$2\ \mathrm{m/s^2$}. $$What does the scale read?

Accepted Answer

$$N = m(g + a) = 70 	imes (9.8 + 2) = 826\ \mathrm{N}$$

Question 4

A 2 kg object is thrown straight up with an initial speed of $$20\ \mathrm{m/s}. $$What is its kinetic energy when it reaches a height of $$15\ \mathrm{m}$$? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$KE = \frac{1}{2}mv_0$^2 - mgh = 400 - 294 = 106\ \mathrm{J}$$

Question 5

A 0.5 kg block slides on a frictionless track from a height of $$2\ \mathrm{m}$$ and reaches a lower point at $$0.5\ \mathrm{m}. $$What is its speed at the lower point? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2g(h_1$ - h_2$)} = \sqrt{2 	imes 9.8 	imes (2 - 0.5)} = 5.42\ \mathrm{m/s}$$

Question 6

A 1 kg object falls from a height of $$10\ \mathrm{m}$$ and hits the ground at $$12\ \mathrm{m/s}. $$How much work was done by air resistance?

Accepted Answer

$$W_{nc} = \Delta KE + \Delta PE = \frac{1}{2} 	imes 1 	imes 12^2$ - 0 + 0 - 1 	imes 9.8 	imes 10 = 72 - 98 = -26\ \mathrm{J}$$

Question 7

A 3 kg object moving at $$6\ \mathrm{m/s}$$ slides to a stop over $$9\ \mathrm{m}$$ due to friction. What is the magnitude of the friction force?

Accepted Answer

$$f = \frac{\frac{1}{2}mv^2$}{d} = \frac{0.5 	imes 3 	imes 36}{9} = 6\ \mathrm{N}$$

Question 8

Two carts, one of mass $$2\ \mathrm{kg}$$ moving at $$3\ \mathrm{m/s}$$ and another of mass $$1\ \mathrm{kg} at $$rest, collide and stick together. What is their final velocity?

Accepted Answer

$$v_f = \frac{2 	imes 3 + 1 	imes 0}{2 + 1} = 2\ \mathrm{m/s}$$

Question 9

Two masses, $$M_1 = 4$$\ \mathrm{kg}$$ and M_2$ = 16\ \mathrm{kg}$$, are placed $$10\ \mathrm{m}$$ apart. At what distance from $$M_1$$ should a third mass be placed so that the net gravitational force on it is zero?

Accepted Answer

$$x = \frac{10}{1 + \sqrt{M_2$/M_1$}} = \frac{10}{1 + 2} = 3.33\ \mathrm{m}$$

Question 10

A figure skater spins with an angular speed $$\$$omega_0$$ and moment of inertia I_0$. She pulls her arms in, reducing her moment of inertia to I = 0.5I_0$. What is her new angular speed?

Accepted Answer

$$\omega = \frac{I_0$}{I} \$$omega_0$$ = 2\$$omega_0$$

Question 11

A string of length $$1.2\ \mathrm{m} is $$vibrating in its second harmonic with a frequency of $$60\ \mathrm{Hz}. $$What is the speed of the wave on the string?

Accepted Answer

$$v = 2Lf = 2 	imes 1.2 	imes 60 = 144\ \mathrm{m/s}$$

Question 12

A wave on a wire has a wavelength of $$0.5\ \mathrm{m}$$ and a period of $$0.01\ \mathrm{s}. $$What is the speed of the wave?

Accepted Answer

$$v = \lambda / T = 0.5 / 0.01 = 50\ \mathrm{m/s}$$

Question 13

For a block attached to a spring undergoing simple harmonic motion, which of the following is true about the force, acceleration, and kinetic energy as a function of displacement $$x$$ from equilibrium?

Accepted Answer

Force and acceleration are proportional to $$-x$$, kinetic energy is maximum at $$x = 0$$

Question 14

A massless see-saw is balanced with a $$30\ \mathrm{kg}$$ child sitting $$2\ \mathrm{m}$$ from the pivot on one side. Where should a $$20\ \mathrm{kg}$$ child sit on the other side to balance the see-saw?

Accepted Answer

$$x = \frac{30 	imes 2}{20} = 3\ \mathrm{m}$$

Question 15

An object weighs $$10\ \mathrm{N} in $$air and $$8\ \mathrm{N}$$ when fully submerged in water. What is the density of the object? (Density of water $$= 1000\ \mathrm{kg/m^3$}$$, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$ho = \frac{W_{air}}{W_{air} - W_{water}} ho_{water} = \frac{10}{2} 	imes 1000 = 5000\ \mathrm{kg/m^3$}$$

Question 16

A gas expands at constant pressure, absorbing $$500\ \mathrm{J} of $$heat and doing $$300\ \mathrm{J} of $$work. What is the change in internal energy of the gas?

Accepted Answer

$$\Delta U = Q - W = 500 - 300 = 200\ \mathrm{J}$$

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