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 time it takes for the ball to reach the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$t = \sqrt{\dfrac{2h}{g}} = \sqrt{\dfrac{2 \times 45}{9.8}} \approx 3.03\ \mathrm{s}$$

Q: A car of mass $$1200\ \mathrm{kg} is $$moving at $$20\ \mathrm{m/s} on a $$flat road. If the coefficient of kinetic friction between the tires and the road is $$\mu_k = 0.7$$, what is the minimum stopping distance when the brakes are applied?

$$d = \dfrac{v^2$}{2\mu_k g} = \dfrac{(20)^2$}{2 \times 0.7 \times 9.8} \approx 29.1\ \mathrm{m}$$

Q: A projectile is launched from the ground with an initial speed of $$30\ \mathrm{m/s} at an $$angle of $$45^\circ$$ above the horizontal. What is the maximum height reached by the projectile? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$h_{max} = \dfrac{v_0$^2 \sin^2$\theta}{2g} = \dfrac{(30)^2$ \times (\sin 45^\$$circ)^2$$}{2 \times 9.8} \approx 22.96\ \mathrm{m}$$

Q: A 2 kg block slides down a frictionless incline of height 5 m. What is its speed at the bottom of the incline?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5} \approx 9.9\ \mathrm{m/s}$$

Q: A 3 kg object is attached to a string and swung in a horizontal circle of radius 2 m at a constant speed of $$6\ \mathrm{m/s}. $$What is the tension in the string?

$$T = m\dfrac{v^2$}{r} = 3 \times \dfrac{6^2$}{2} = 54\ \mathrm{N}$$

Q: A hydraulic lift uses a small piston of area $$0.01\ \mathrm{m^2$} to $$lift a car with a large piston of area $$0.5\ \mathrm{m^2$}. If a $$force of $$200\ \mathrm{N} is $$applied to the small piston, what is the maximum weight of the car that can be lifted? (Neglect the weight of the pistons and fluid.)

$$F_{car} = F_{small} \dfrac{A_{large}}{A_{small}} = 200 \times \dfrac{0.5}{0.01} = 10,000\ \mathrm{N}$$

Q: A 1.5 kg object is moving in a circle of radius 0.75 m at a constant angular speed. If the object completes one revolution every 2 seconds, what is the magnitude of the centripetal force acting on it?

$$F_c = m \dfrac{v^2$}{r} = 1.5 \times \dfrac{(2.36)^2$}{0.75} \approx 7.45\ \mathrm{N}$$

Q: A 0.2 kg ball is attached to a string and swung in a vertical circle of radius 1.5 m. What is the minimum speed at the top of the circle so that the string remains taut?

$$v_{min} = \sqrt{g r} = \sqrt{9.8 \times 1.5} \approx 3.83\ \mathrm{m/s}$$

Q: A 5 kg box is pulled up a rough incline (angle $$30^\circ) at $$constant speed. If the coefficient of kinetic friction is $$0.2$$, what is the magnitude of the pulling force parallel to the incline? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$F = mg \sin\theta + \mu_k mg \cos\theta = 5 \times 9.8 \times \sin 30^\circ + 0.2 \times 5 \times 9.8 \times \cos 30^\circ \approx 24.5 + 8.5 = 33.0\ \mathrm{N}$$

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 time it takes for the ball to reach the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}} = \sqrt{\dfrac{2 	imes 45}{9.8}} \approx 3.03\ \mathrm{s}$$

Question 2

A car of mass $$1200\ \mathrm{kg} is $$moving at $$20\ \mathrm{m/s} on a $$flat road. If the coefficient of kinetic friction between the tires and the road is $$\mu_k = 0.7$$, what is the minimum stopping distance when the brakes are applied?

Accepted Answer

$$d = \dfrac{v^2$}{2\mu_k g} = \dfrac{(20)^2$}{2 	imes 0.7 	imes 9.8} \approx 29.1\ \mathrm{m}$$

Question 3

A projectile is launched from the ground with an initial speed of $$30\ \mathrm{m/s} at an $$angle of $$45^\circ$$ above the horizontal. What is the maximum height reached by the projectile? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h_{max} = \dfrac{v_0$^2 \sin^2$	heta}{2g} = \dfrac{(30)^2$ 	imes (\sin 45^\$$circ)^2$$}{2 	imes 9.8} \approx 22.96\ \mathrm{m}$$

Question 4

A 2 kg block slides down a frictionless incline of height 5 m. What is its speed at the bottom of the incline?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 5} \approx 9.9\ \mathrm{m/s}$$

Question 5

A 0.5 kg ball moving at $$4\ \mathrm{m/s}$$ collides elastically with a stationary 0.5 kg ball. What is the velocity of the first ball after the collision?

Accepted Answer

$$v_{1f} = 0\ \mathrm{m/s}$$

Question 6

A 3 kg object is attached to a string and swung in a horizontal circle of radius 2 m at a constant speed of $$6\ \mathrm{m/s}. $$What is the tension in the string?

Accepted Answer

$$T = m\dfrac{v^2$}{r} = 3 	imes \dfrac{6^2$}{2} = 54\ \mathrm{N}$$

Question 7

A hydraulic lift uses a small piston of area $$0.01\ \mathrm{m^2$} to $$lift a car with a large piston of area $$0.5\ \mathrm{m^2$}. If a $$force of $$200\ \mathrm{N} is $$applied to the small piston, what is the maximum weight of the car that can be lifted? (Neglect the weight of the pistons and fluid.)

Accepted Answer

$$F_{car} = F_{small} \dfrac{A_{large}}{A_{small}} = 200 	imes \dfrac{0.5}{0.01} = 10,000\ \mathrm{N}$$

Question 8

A 1.5 kg object is moving in a circle of radius 0.75 m at a constant angular speed. If the object completes one revolution every 2 seconds, what is the magnitude of the centripetal force acting on it?

Accepted Answer

$$F_c = m \dfrac{v^2$}{r} = 1.5 	imes \dfrac{(2.36)^2$}{0.75} \approx 7.45\ \mathrm{N}$$

Question 9

A 0.2 kg ball is attached to a string and swung in a vertical circle of radius 1.5 m. What is the minimum speed at the top of the circle so that the string remains taut?

Accepted Answer

$$v_{min} = \sqrt{g r} = \sqrt{9.8 	imes 1.5} \approx 3.83\ \mathrm{m/s}$$

Question 10

A 5 kg box is pulled up a rough incline (angle $$30^\circ) at $$constant speed. If the coefficient of kinetic friction is $$0.2$$, what is the magnitude of the pulling force parallel to the incline? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$F = mg \sin	heta + \mu_k mg \cos	heta = 5 	imes 9.8 	imes \sin 30^\circ + 0.2 	imes 5 	imes 9.8 	imes \cos 30^\circ \approx 24.5 + 8.5 = 33.0\ \mathrm{N}$$

Question 11

A 0.3 kg object is dropped into a 0.5 kg calorimeter containing 0.2 kg of water at $$20^\circ\mathrm{C}. If $$the object is initially at $$100^\circ\mathrm{C}$$ and the final equilibrium temperature is $$25^\circ\mathrm{C}$$, what is the specific heat capacity of the object? (Assume $$c_{water} = 4186\ \mathrm{J/kg\cdot K}$$, calorimeter does not absorb heat.)

Accepted Answer

$$c = \dfrac{m_{water} c_{water} (T_f - T_{water})}{m_{obj} (T_{obj} - T_f)} = \dfrac{0.2 	imes 4186 	imes (25 - 20)}{0.3 	imes (100 - 25)} \approx 186\ \mathrm{J/kg\cdot K}$$

Question 12

A gas in a sealed, rigid container is heated from $$300\ \mathrm{K} to$$ $$600\ \mathrm{K}. If $$the initial pressure is $$100\ \mathrm{kPa}$$, what is the final pressure? (Assume ideal gas behavior.)

Accepted Answer

$$P_2$$ = $$P_1$$ \dfrac{$$T_2$$}{$$T_1$$} = 100 	imes \dfrac{600}{300} = 200\ \mathrm{kPa}$$

Question 13

A 0.4 kg mass attached to a spring oscillates with a period of $$0.8\ \mathrm{s}. $$What is the spring constant $$k$$?

Accepted Answer

$$k = \dfrac{4\pi^2$ m}{T^2$} = \dfrac{4 	imes \pi^2$ 	imes 0.4}{(0.8)^2$} \approx 24.7\ \mathrm{N/m}$$

Question 14

A 2 kg object moving at $$5\ \mathrm{m/s}$$ collides inelastically with a 3 kg object at rest. What is their final velocity after the collision?

Accepted Answer

$$v_f = \dfrac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \dfrac{2 	imes 5 + 3 	imes 0}{2 + 3} = 2\ \mathrm{m/s}$$

Question 15

A nurse uses a syringe to inject medicine into a patient. If the nurse applies a force of $$5\ \mathrm{N} to $$the plunger with an area of $$2 	imes 10$$^{-4}$$\ \mathrm{m^2$}$$, what is the pressure exerted by the fluid?

Accepted Answer

$$P = \dfrac{F}{A} = \dfrac{5}{2 	imes 10$$^{-4}$$} = 25,000\ \mathrm{Pa}$$

Question 16

A 0.5 kg mass is attached to a string and swung in a horizontal circle of radius 1.2 m at a speed of $$3\ \mathrm{m/s}. $$What is the period of revolution?

Accepted Answer

$$T = \dfrac{2\pi r}{v} = \dfrac{2 \pi 	imes 1.2}{3} \approx 2.51\ \mathrm{s}$$

Question 17

A 1.0 kg block is attached to a horizontal spring (spring constant $$k = 50\ \mathrm{N/m}) $$and oscillates with amplitude $$0.2\ \mathrm{m}. $$What is the maximum kinetic energy of the block?

Accepted Answer

$$K_{max} = \dfrac{1}{2} k A^2$ = \dfrac{1}{2} 	imes 50 	imes (0.2)^2$ = 1.0\ \mathrm{J}$$

Question 18

A 0.6 kg ball is dropped from rest from a height of 2 m onto a hard floor. If the ball rebounds to a height of 1.5 m, what is the energy lost during the bounce?

Accepted Answer

$$\Delta E = m g (h_{initial} - h_{final}) = 0.6 	imes 9.8 	imes (2 - 1.5) = 2.94\ \mathrm{J}$$

Physics 20: General Physics I - Course Structure, Topics, and Learning Outcomes

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