Question 1

A block is acted upon by two forces: $$\vec{F}_1 = (3.0\ \mathrm{N})\ \hat{i} + (4.0\ \mathrm{N})\ \hat{j}$$ and $$\vec{F}_2 = (-3.0\ \mathrm{N})\ \hat{i} + (4.0\ \mathrm{N})\ \hat{j}. If $$the block has a mass of $$2.0\ \mathrm{kg}$$, what is the magnitude of its acceleration?

Accepted Answer

$$2.8\ \mathrm{m/s^2$}$$

Question 2

Two horizontal forces act on a $$3.0\ \mathrm{kg}$$ object on a frictionless surface. $$\vec{F}_1 = 9.0\ \mathrm{N}$$ east, $$\vec{F}_2 = 8.0\ \mathrm{N}$$ acting $$62^\circ$$ north of west. What is the direction of the net force relative to east?

Accepted Answer

$$19^\circ$$ north of west

Question 3

A $$2.0\ \mathrm{kg}$$ object moves along the $$x-$$axis, propelled by a force $$F = 3.0t + 0.4t^2$ - 0.2t^3$ (in N) where t$ is in seconds. At t = 3.0$$\ \mathrm{s}$$, what is the magnitude of the acceleration?

Accepted Answer

$$1.2\ \mathrm{m/s^2$}$$

Question 4

A $$2.0\ \mathrm{kg}$$ object is moving along the $$x-$$axis under a force $$F = 3.0t + 0.4t^2$ - 0.2t^3$ (in N). At t = 3.0$$\ \mathrm{s}$$, the velocity is -3.6$$\ \mathrm{m/s}$$ in the negative x$-direction. What is the value of the constant c$ in the position function x = 3.0t$$ + $$0.4t^2$$ + $$ct^3$$?

Accepted Answer

$$-0.2$$

Question 5

In a system where four disks are suspended by cords, the top cord supports the weight of all disks. If $$T_1 = 60$$\ \mathrm{N}$$, T_2$ = 50\ \mathrm{N}$$, and $$T_3 = 10$$\ \mathrm{N}$$, what is the mass of disk B$?

Accepted Answer

$$5.1\ \mathrm{kg}$$

Question 6

In the same four-disk arrangement, what is the tension in the cord just above disk $$C if$$ $$T_2 = 50$$\ \mathrm{N}$$ and T_3$ = 10\ \mathrm{N}$$?

Accepted Answer

$$40\ \mathrm{N}$$

Question 7

An Atwood's machine consists of two blocks, $$m_1 = 1.30$$\ \mathrm{kg}$$ and m_2$ = 2.80\ \mathrm{kg}$$, connected by a cord over a frictionless pulley. What is the acceleration of the system?

Accepted Answer

$$3.9\ \mathrm{m/s^2$}$$

Question 8

For the Atwood's machine above, what is the tension in the cord?

Accepted Answer

$$12.7\ \mathrm{N}$$

Question 9

In the Atwood's machine, if $$m_1$$ = $$m_2$$, what is the acceleration of the system?

Accepted Answer

$$0$$

Question 10

Three masses $$m_1 = 30$$\ \mathrm{kg}$$, m_2$ = 40\ \mathrm{kg}$$, and $$m_3 = 10$$\ \mathrm{kg}$$ are connected by cords on a frictionless table, with m_3$ hanging off the edge. What is the acceleration of the system?

Accepted Answer

$$0.98\ \mathrm{m/s^2$}$$

Question 11

In the three-mass system above, what is the tension in the cord connecting blocks $$B$$ and $$C$$ ($$m_2$$ and $$m_3$$)?

Accepted Answer

$$8.8\ \mathrm{N}$$

Question 12

A $$10\ \mathrm{kg}$$ block is pulled across a frictionless surface by a $$40\ \mathrm{N}$$ force at $$30^\circ$$ above the horizontal. What is the block's acceleration?

Accepted Answer

$$3.46\ \mathrm{m/s^2$}$$

Question 13

A $$5.0\ \mathrm{kg}$$ object is suspended by a rope. If the tension in the rope is $$60\ \mathrm{N}$$, what is the acceleration of the object?

Accepted Answer

$$2.2\ \mathrm{m/s^2$}$$\ upward

Question 14

A $$2.0\ \mathrm{kg}$$ block is acted on by a force $$\vec{F} = (6.0\ \mathrm{N})\ \hat{i} + (8.0\ \mathrm{N})\ \hat{j}. $$What is the magnitude of the block's acceleration?

Accepted Answer

$$7.2\ \mathrm{m/s^2$}$$

Question 15

A $$3.0\ \mathrm{kg}$$ object is moving on a horizontal surface with negligible friction. If a $$9.0\ \mathrm{N}$$ force acts east and an $$8.0\ \mathrm{N}$$ force acts $$62^\circ$$ north of west, what is the magnitude of the object's acceleration?

Accepted Answer

$$3.1\ \mathrm{m/s^2$}$$

Question 16

A $$1.0\ \mathrm{kg}$$ block is pulled by a $$10.0\ \mathrm{N}$$ force on a frictionless table. What is the block's velocity after $$2.0\ \mathrm{s} if it $$starts from rest?

Accepted Answer

$$20.0\ \mathrm{m/s}$$

Question 17

A $$2.0\ \mathrm{kg}$$ object is subjected to a force $$\vec{F} = (3.0\ \mathrm{N})\ \hat{i} + (4.0\ \mathrm{N})\ \hat{j}. $$What is the direction of the acceleration vector relative to the $$x-$$axis?

Accepted Answer

$$53^\circ$$ above the $$x-$$axis

Question 18

A $$10.0\ \mathrm{kg}$$ block is pulled by a rope with a tension of $$40.0\ \mathrm{N} at an $$angle of $$30^\circ$$ above the horizontal. What is the vertical component of the tension?

Accepted Answer

$$20.0\ \mathrm{N}$$

Dynamics and Forces: Study Notes for College Physics

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