Q: A projectile is launched with initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the maximum height reached by the projectile?

$$h_{max} = \frac{v_0$^2 \sin^2$ \theta}{2g}$$

Question 1

A block slides on a horizontal surface and slows uniformly (constant acceleration) to stop. Its initial speed is 15.0 cm/s and the distance it moves is 28.0 cm. How long did it take to travel the 28.0 cm?

Accepted Answer

$$t = 1.87 \ \mathrm{s}$$

Question 2

A ball is shot at a speed $$v_0 at$$ $$25^\circ$$ above the horizontal. Let $$x be $$the horizontal direction and $$y$$ the vertical direction. If the ball hits at position $$(0, m)$$ and 2.86 s later passes through the position $$(107.4 \ \mathrm{m}, 10.0 \ \mathrm{m})$$, find the initial speed $$v_0.$$

Accepted Answer

$$v_0 = 42.63$$ \ \mathrm{m/s}$$

Question 3

A 100 kg box sits in an elevator on top of a scale. What does the scale read if the elevator is accelerating upward at $$3.0 \ \mathrm{m/s^2$}$$?

Accepted Answer

$$1290 \ \mathrm{N}$$

Question 4

A 10 kg flower pot hangs from a wire from the middle of a ceiling. The ends of the wire are attached to opposite sides of a small room and the wire sags down in the middle making an angle $$	heta$$ with respect to the horizontal. If the tension in the wire is $$500.0 \ \mathrm{N}$$, what is the angle $$	heta$$?

Accepted Answer

$$11.3^\circ$$

Question 5

A 2.0 kg ball attached to a 1.5 m string swings in a vertical circle. At the top of the circle the speed of the ball is $$5.5 \ \mathrm{m/s}. $$What is the tension in the string when the ball is at the top of the circle?

Accepted Answer

$$60.27 \ \mathrm{N}$$

Question 6

Three blocks are arranged as shown. They are near to the surface of the Earth and, due to a force $$F on $$the bottom block, all three accelerate upward at $$4.1 \ \mathrm{m/s^2$}$$. $$m_1 = 1.0$$ \ \mathrm{kg}$$, m_2$ = 3.0 \ \mathrm{kg}$$, $$m_3 = 5.0$$ \ \mathrm{kg}$$. What force is exerted on the bottom block by the middle block? Give the size and the direction.

Accepted Answer

$$55.6 \ \mathrm{N}$$ \ downward

Question 7

A car moves at a steady speed of $$30.0 \ \mathrm{m/s}$$ for $$4.1 \ \mathrm{s}. It $$then slows to a stop with an acceleration of $$-6.3 \ \mathrm{m/s^2$}. $$What is the total distance travelled?

Accepted Answer

$$194.4 \ \mathrm{m}$$

Question 8

Two point masses, A and B, are in the x-y plane. Find the force exerted by mass A on mass B. Express your answer in component form. $$m_A = 4.2 	imes 10^6$ \ \mathrm{kg} at$$ $$(0, 2.0 \ \mathrm{m})$$, $$m_B = 5.7 	imes 10^6$ \ \mathrm{kg} at$$ $$(5.7 \ \mathrm{m}, 7.3 \ \mathrm{m}).$$

Accepted Answer

$$\vec{F}_{AB} = (21.8 \hat{i} + 33.1 \hat{j}) \ \mathrm{N}$$

Question 9

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

Accepted Answer

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

Question 10

A projectile is launched with initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the maximum height reached by the projectile?

Accepted Answer

$$h_{max} = \frac{v_0$^2 \sin^2$ 	heta}{2g}$$

Question 11

A 5.0 kg object is pulled by a force of $$20 \ \mathrm{N} at an $$angle of $$30^\circ$$ above the horizontal. What is the horizontal component of the force?

Accepted Answer

$$F_x = 17.32 \ \mathrm{N}$$

Question 12

A ball is thrown vertically upward with initial speed $$v_0. $$What is the time to reach the maximum height?

Accepted Answer

$$t = \frac{v_0$}{g}$$

Question 13

A 2.0 kg block is attached to a spring with spring constant $$k = 50 \ \mathrm{N/m}$$ and oscillates on a frictionless surface. What is the period of oscillation?

Accepted Answer

$$T = 1.26 \ \mathrm{s}$$

Question 14

A 3.0 kg object is dropped from a height of 10 m. What is its speed just before hitting the ground?

Accepted Answer

$$v = 14.0 \ \mathrm{m/s}$$

Question 15

A 1.0 kg mass is attached to a string and swung in a horizontal circle of radius 2.0 m at a speed of 4.0 m/s. What is the tension in the string?

Accepted Answer

$$T = 8.0 \ \mathrm{N}$$

Question 16

A 0.5 kg ball is dropped from rest and takes 2.0 s to reach the ground. What is the height from which it was dropped?

Accepted Answer

$$h = 19.6 \ \mathrm{m}$$

Question 17

A 2.0 kg block slides down a frictionless ramp of length 5.0 m inclined at $$30^\circ. $$What is its speed at the bottom?

Accepted Answer

$$v = 7.0 \ \mathrm{m/s}$$

Exam 1 from last yr study guide

Guida di studio - Domande di pratica

Study guide - Flashcard