Q: Water ($$\rho = 1000\ \mathrm{kg/m^3$}) $$flows through a horizontal pipe. In the wider section, the cross-sectional area is $$0.30\ \mathrm{m}^2$$, the speed is $$2.0\ \mathrm{m/s}$$, and the pressure is $$150,000\ \mathrm{Pa}. $$The pipe narrows to $$0.10\ \mathrm{m}^2. $$Assuming ideal fluid behavior, what’s the pressure in the narrow section?

$$1.3 \times 10^5$\ \mathrm{Pa}$$

Question 1

A vector $$ \vec{A} = -3 \hat{i} + 0 \hat{j} + 2 \hat{k} $$ and $$ \vec{B} = -1 \hat{i} -1 \hat{j} + 1 \hat{k} . $$What is the value of the dot product $$ \vec{A} \cdot \vec{B} $$?

Accepted Answer

$$5$$

Question 2

A test rocket is fired straight up from rest with a net acceleration of $$20.0\ \mathrm{m/s^2$}. $$After $$4.00\ \mathrm{s}$$ the motor turns off, but the rocket continues to coast upward with no appreciable air resistance. What maximum elevation does the rocket reach?

Accepted Answer

$$487\ \mathrm{m}$$

Question 3

Convert a speed of $$4.50\ \mathrm{km/h} to $$units of $$\mathrm{ft/min}$$. ($$1.00\ \mathrm{m} = 3.28\ \mathrm{ft})$$

Accepted Answer

$$246\ \mathrm{ft/min}$$

Question 4

A swimmer heads directly across a river $$200\ \mathrm{m}$$ wide and reaches the opposite bank in $$6$$ min $$40 s$$, during which time she is swept downstream $$480\ \mathrm{m}. $$What is the speed of the current?

Accepted Answer

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

Question 5

A block of mass $$m is on a $$frictionless table and is attached to a rope that passes over a massless, frictionless pulley to a hanging mass $$M. $$The system is released from rest. What is the magnitude of the tension in the rope?

Accepted Answer

$$\frac{mMg}{m+M}$$

Question 6

A $$0.40\ \mathrm{kg}$$ puck on a horizontal frictionless surface experiences a time-dependent horizontal force $$F(t) = (6\ \mathrm{N/s}) t$$, where $$t is in $$seconds. If the puck is initially at rest, what is its speed after $$3.0\ \mathrm{s}$$?

Accepted Answer

$$67.5\ \mathrm{m/s}$$

Question 7

A block is pulled at constant speed up a rough ramp by a rope parallel to the ramp. Which of the following changes will decrease the amount of tension needed to keep the speed constant?

Accepted Answer

Decreasing the ramp angle while keeping the friction the same

Question 8

A force $$\vec{F} = (3\hat{i} + 4\hat{j})\ \mathrm{N}$$ acts on a particle that moves from position $$\vec{r}_1 = (1\hat{i} + 2\hat{j})\ \mathrm{m} to$$ $$\vec{r}_2 = (4\hat{i} + 6\hat{j})\ \mathrm{m}. $$What is the work done by the force?

Accepted Answer

$$25\ \mathrm{J}$$

Question 9

A block slides down a rough inclined plane with constant velocity. Which of the following statements is true?

Accepted Answer

The net work done on the block is zero.

Question 10

A variable force $$F(x) = 6x^2$ (in newtons, where x$ is in meters) acts on a particle moving along the x$-axis. What is the work done by this force as the particle moves from x = 1$$\ \mathrm{m}$$ to x = 3$$\ \mathrm{m}$$?

Accepted Answer

$$52\ \mathrm{J}$$

Question 11

A ball is released from rest on a no-slip surface. After reaching its lowest point, the ball begins to rise again, this time on a frictionless surface. When the ball reaches its maximum height on the frictionless surface, it is

Accepted Answer

at a lesser height than when it was released.

Question 12

A solid sphere with uniform density, mass $$2.0\ \mathrm{kg}$$, and radius $$0.50\ \mathrm{m}$$, rotating at constant angular velocity about a stationary axis through its diameter, has a kinetic energy of $$10\ \mathrm{J}. $$What is the tangential velocity of a point on the equator?

Accepted Answer

$$5\ \mathrm{m/s}$$

Question 13

A steel wire with a cross-sectional area of $$0.10\ \mathrm{m}^2$$ and a length of $$70.0\ \mathrm{m} is $$stretched by $$0.50\ \mathrm{m}. $$What is the tensile strain on the wire?

Accepted Answer

$$7.14 	imes 10$$^{-3}$$

Question 14

A cup of water containing an ice cube at $$0^\circC is $$filled to the brim. The tip of the ice cube sticks out of the surface. As the ice melts, you observe that

Accepted Answer

the water level remains the same.

Question 15

Water ($$\rho = 1000\ \mathrm{kg/m^3$}) $$flows through a horizontal pipe. In the wider section, the cross-sectional area is $$0.30\ \mathrm{m}^2$$, the speed is $$2.0\ \mathrm{m/s}$$, and the pressure is $$150,000\ \mathrm{Pa}. $$The pipe narrows to $$0.10\ \mathrm{m}^2. $$Assuming ideal fluid behavior, what’s the pressure in the narrow section?

Accepted Answer

$$1.3 	imes 10^5$\ \mathrm{Pa}$$

PHYS 170 Exam Study Guide: Vectors, Kinematics, Dynamics, Energy, Rotation, and Fluids

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