Q: A uniform beam of length 4 m and mass 20 kg is supported at its ends. A 60 kg person stands 1 m from the left end. What is the force exerted by the right support?

$$F_{\text{right}} = 245\ \mathrm{N}$$

Q: A force of $$1000\ \mathrm{N} is $$applied to a steel rod of cross-sectional area $$2 \times 10$$^{-4}$$\ \mathrm{m^2$}$$ and length $$2\ \mathrm{m}. If $$the Young's modulus for steel is $$2 \times 10$$^{11}$$\ \mathrm{N/m^2$}$$, what is the elongation of the rod?

$$\Delta l = 5 \times 10$$^{-6}$$\ \mathrm{m}$$

Question 1

A car accelerates uniformly from rest and travels a distance of 200 m in 10 s. What is the magnitude of its acceleration?

Accepted Answer

$$a = 2.0\ \mathrm{m/s^2$}$$

Question 2

A projectile is launched from the ground with an initial speed $$v_0 = 20$$\ \mathrm{m/s}$$ at an angle $$\$$theta_0 = 30$$^\circ$$ above the horizontal. What is the range of the projectile (assume it lands at the same height)?

Accepted Answer

$$R = 40.8\ \mathrm{m}$$

Question 3

A 5 kg block is pulled across a horizontal surface with a constant velocity by a horizontal force of 20 N. What is the coefficient of kinetic friction between the block and the surface?

Accepted Answer

$$\mu_k = 0.40$$

Question 4

A satellite orbits Earth at a radius $$r = 2R_{	ext{Earth}}. $$What is its orbital speed? (Let $$v_0 be $$the orbital speed at Earth's surface.)

Accepted Answer

$$v = \dfrac{v_0$}{\sqrt{2}}$$

Question 5

A force $$\vec{F} = (3\hat{i} + 4\hat{j})\ \mathrm{N}$$ moves an object from point $$A(0,0) to$$ $$B(2,3)$$ meters. What is the work done by the force?

Accepted Answer

$$W = 18\ \mathrm{J}$$

Question 6

A 2 kg mass is attached to a spring with $$k = 50\ \mathrm{N/m}$$ and is compressed by 0.1 m from equilibrium. What is the elastic potential energy stored in the spring?

Accepted Answer

$$U = 0.50\ \mathrm{J}$$

Question 7

A 3 kg object moving at $$4\ \mathrm{m/s}$$ collides elastically with a stationary 1 kg object. What is the final velocity of the 3 kg object after the collision?

Accepted Answer

$$v' = 2\ \mathrm{m/s}$$

Question 8

A disk of mass $$2\ \mathrm{kg}$$ and radius $$0.5\ \mathrm{m}$$ rotates about its center with angular speed $$\omega = 4\ \mathrm{rad/s}. $$What is its rotational kinetic energy?

Accepted Answer

$$K = 8\ \mathrm{J}$$

Question 9

A uniform beam of length 4 m and mass 20 kg is supported at its ends. A 60 kg person stands 1 m from the left end. What is the force exerted by the right support?

Accepted Answer

$$F_{	ext{right}} = 245\ \mathrm{N}$$

Question 10

A solid sphere (mass $$m$$, radius $$R) $$rolls without slipping down an incline of height $$h. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{\dfrac{10gh}{7}}$$

Question 11

A 1.5 kg object is whirled in a horizontal circle of radius 2 m at a speed of 3 m/s. What is the magnitude of the required centripetal force?

Accepted Answer

$$F_c = 6.75\ \mathrm{N}$$

Question 12

A 0.5 kg ball is dropped from a height of 10 m. What is its speed just before hitting the ground? (Ignore air resistance.)

Accepted Answer

$$v = 9.9\ \mathrm{m/s}$$

Question 13

A 1000 kg car moving at $$20\ \mathrm{m/s}$$ comes to a stop in 5 s due to a constant braking force. What is the magnitude of the braking force?

Accepted Answer

$$F = 4000\ \mathrm{N}$$

Question 14

A 2 kg object is moving with velocity $$\vec{v} = (3\hat{i} - 4\hat{j})\ \mathrm{m/s}. $$What is its linear momentum?

Accepted Answer

$$\vec{p} = (6\hat{i} - 8\hat{j})\ \mathrm{kg\cdot m/s}$$

Question 15

A force of $$1000\ \mathrm{N} is $$applied to a steel rod of cross-sectional area $$2 	imes 10$$^{-4}$$\ \mathrm{m^2$}$$ and length $$2\ \mathrm{m}. If $$the Young's modulus for steel is $$2 	imes 10$$^{11}$$\ \mathrm{N/m^2$}$$, what is the elongation of the rod?

Accepted Answer

$$\Delta l = 5 	imes 10$$^{-6}$$\ \mathrm{m}$$

Question 16

A cube of ice (density $$900\ \mathrm{kg/m^3$}$$, side $$0.1\ \mathrm{m}) $$floats in water (density $$1000\ \mathrm{kg/m^3$}). $$What fraction of the ice cube's volume is submerged?

Accepted Answer

$$0.90$$

Question 17

A 2 kg mass is attached to a string and swung in a horizontal circle of radius 1.5 m at a constant speed. If the string makes an angle of $$30^\circ$$ with the vertical, what is the speed of the mass?

Accepted Answer

$$v = 2.89\ \mathrm{m/s}$$

Question 18

A 0.2 kg ball moving at $$5\ \mathrm{m/s}$$ collides head-on and sticks to a 0.3 kg ball initially at rest. What is their common velocity after the collision?

Accepted Answer

$$v = 2.0\ \mathrm{m/s}$$

Question 19

A wheel of radius $$0.4\ \mathrm{m}$$ rotates with a constant angular acceleration of $$2\ \mathrm{$$rad/s^2$$}. If it $$starts from rest, what is its angular velocity after 3 seconds?

Accepted Answer

$$\omega = 6\ \mathrm{rad/s}$$

PHYS1425 Formula Sheet: Mechanics, Energy, and Fluids

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