Q: Refer to the eighth image. A block of mass $$m is on a $$rough incline and is pushed horizontally by force $$P. $$What is the normal force $$N$$ acting on the block?

$$N = mg\cos\theta + P\sin\theta$$

Question 1

A car moves along the x-axis with velocity $$v_x as a $$function of time, as shown in the first image (velocity-time graph). During which time interval does the car move at constant velocity?

Accepted Answer

From $$t = 30 to$$ $$t = 90$$ minutes

Question 2

Refer to the second image (velocity-time graph). What is the acceleration of the particle between $$t = 0$$ and $$t = 2$$ seconds?

Accepted Answer

$$a = -1\ \mathrm{m/s^2$}$$

Question 3

In the third image, a ball is thrown upward with initial velocity $$v_0$$ from the roof of a building of height $$H$$, while a lift next to it moves downward at the same speed $$v_0. $$What is the initial velocity of the ball relative to the lift?

Accepted Answer

$$2v_0$$ upward

Question 4

The fourth image shows the $$x-$$position of a particle as a function of time. What is the average velocity of the particle from $$t = 0 to$$ $$t = 20$$ seconds?

Accepted Answer

Question 5

Refer to the fifth image (projectile motion graph). If the projectile lands at $$x = 80\ \mathrm{m}$$, what is the total time of flight?

Accepted Answer

$$4\ \mathrm{s}$$

Question 6

In the sixth image, a ball is thrown from point $$O$$ and lands on a roof at $$P$$ after $$4$$ seconds. If the vertical velocity component on impact is $$-15\ \mathrm{m/s}$$, what was the initial vertical velocity component?

Accepted Answer

$$25\ \mathrm{m/s}$$

Question 7

In the seventh image, a $$2\ \mathrm{kg}$$ block rests on a rough incline at angle $$	heta$$ ($$	an	heta = 3/4). $$What is the minimum coefficient of static friction $$\mu_s$$ required to keep the block at rest?

Accepted Answer

$$0.75$$

Question 8

Refer to the eighth image. A block of mass $$m is on a $$rough incline and is pushed horizontally by force $$P. $$What is the normal force $$N$$ acting on the block?

Accepted Answer

$$N = mg\cos	heta + P\sin	heta$$

Question 9

In the ninth image, two blocks $$m_1$$ and $$m_2$$ are connected over a pulley on an incline. If $$m_2$$ slides down with acceleration $$a = \frac{2g}{5}$$, and $$\mu_{k1} = 0.4$$, $$\mu_{k2} = 0.5$$, what is $$m_2 in $$terms of $$m if$$ $$m_1 = 2m$?

Accepted Answer

$$m_2 = 26.4m$

Question 10

Refer to the tenth image. Block $$A ($$mass $$m_A) is on a $$table, connected by a string over a pulley to block $$B$$ ($$2\ \mathrm{kg}) $$hanging off the edge. If the coefficient of kinetic friction between $$A$$ and the table is $$\mu_k = 0.25$$, what must $$m_A be $$for $$A to $$move right at constant velocity?

Accepted Answer

$$m_A = 8\ \mathrm{kg}$$

Question 11

In the eleventh image, block $$m_1 = 20$$\ \mathrm{kg}$$ is connected by a string to block m_2$ = 5\ \mathrm{kg}$$ over a pulley. The coefficient of kinetic friction between $$m_1$$ and the surface is $$\mu_k = 0.3. $$What is the acceleration of $$m_1$$?

Accepted Answer

$$a = 1\ \mathrm{m/s^2$}$$

Question 12

Refer to the twelfth image. Blocks $$m_1$$ and $$m_2$$ are stacked, with $$m_1$$ tied to $$m_3$$ over a pulley. If $$\mu_s = 0.5$$ between $$m_1$$ and $$m_2$$, what is the acceleration $$a$$ when $$m_2 is $$just about to slip on $$m_1$$?

Accepted Answer

$$a = 5\ \mathrm{m/s^2$}$$

Question 13

In the thirteenth image, a roller-coaster car of mass $$1200\ \mathrm{kg}$$ moves at constant speed around a loop of radius $$10\ \mathrm{m}. $$What is the minimum speed at the highest point $$C to $$complete the loop?

Accepted Answer

$$v = 10\ \mathrm{m/s}$$

Question 14

Refer to the fourteenth image. A $$20\ \mathrm{kg}$$ child rides a Ferris wheel of radius $$10\ \mathrm{m} at$$ $$5\ \mathrm{m/s}. $$What is the normal force on the child at the top of the wheel?

Accepted Answer

$$N = 150\ \mathrm{N}$$

Question 15

In the fifteenth image, a $$2.0\ \mathrm{kg}$$ block slides down a smooth track from height $$h$$ and crosses a rough section ($$\mu_k = 0.1) of $$length $$2\ \mathrm{m}. $$What is the work done by friction along the rough section?

Accepted Answer

$$-4\ \mathrm{J}$$

Question 16

Refer to the sixteenth image. A $$10\ \mathrm{kg}$$ ball is attached to a $$2\ \mathrm{m}$$ rod and swings from horizontal to the lowest point. What is the work done by gravity from $$A to$$ $$B$$?

Accepted Answer

$$200\ \mathrm{J}$$

Question 17

In the seventeenth image, a $$2\ \mathrm{kg}$$ block slides down a $$30^\circ$$ incline and stretches a spring ($$k = 120\ \mathrm{N/m}). $$What is the change in spring potential energy when the block stops after distance $$d$$?

Accepted Answer

$$\Delta U_s = 60d^2$

Question 18

Refer to the eighteenth image. A $$5.0\ \mathrm{kg}$$ block moves on a smooth floor under a variable force $$F(x) as $$shown. What is the total work done over $$0 \leq x \leq 8\ \mathrm{m}$$?

Accepted Answer

$$25\ \mathrm{J}$$

Question 19

In the nineteenth image, a $$10\ \mathrm{kg}$$ mass slides down a $$2\ \mathrm{m}$$ incline and then moves along a horizontal surface with $$\mu_k = 0.25$$ until it stops. What is the length $$BC$$?

Accepted Answer

$$8\ \mathrm{m}$$

Physics with Calculus: 1D Motion & Relative Motion – Graph Interpretation and Kinematics.

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