Q: A $$62\ \mathrm{kg}$$ person sits on a $$4.0\ \mathrm{kg}$$ chair with four legs. Each leg contacts the floor in a circle of $$1.5\ \mathrm{cm}$$ diameter. What is the pressure exerted on the floor by each leg?

$$9.2 \times 10^5$\ \mathrm{Pa}$$

Q: Superman drinks water through a straw of length $$l = 8.0\ \mathrm{m}. $$What is the water pressure at the top of the straw? ($$\rho = 1000\ \mathrm{kg/m^3$}$$, $$1\ \mathrm{atm} = 1.01 \times 10^5$\ \mathrm{Pa})$$

$$2.26 \times 10^4$\ \mathrm{Pa}$$

Question 1

Is the expression $$\frac{v^2$}{a} = x - \frac{vt}{3}$$ dimensionally correct, where $$x is $$distance, $$a is $$acceleration, $$v is $$velocity, and $$t is $$time?

Accepted Answer

Yes, both sides have dimensions of length.

Question 2

A swimmer starts at $$x = -10.0\ \mathrm{m} at$$ $$t = 0\ \mathrm{s}$$ and reaches $$x = +40.0\ \mathrm{m} at$$ $$t = 25.0\ \mathrm{s}$$, moving at constant velocity. What is the swimmer's position at $$t = 17.0\ \mathrm{s}$$?

Accepted Answer

$$x = 24.0\ \mathrm{m}$$

Question 3

Given the velocity vector $$\vec{v} = 7.5\ \mathrm{m/s} at$$ $$30^\circ$$ clockwise from the positive $$y-$$axis, what is the $$x-$$component of $$\vec{v}$$?

Accepted Answer

$$3.8\ \mathrm{m/s}$$

Question 4

An object is moving with constant velocity. Which of the following best describes the net force acting on the object?

Accepted Answer

No forces are acting on the object.

Question 5

A 123.0 N carton is pulled up a frictionless ramp inclined at $$32.0^\circ by a$$ $$73.4\ \mathrm{N}$$ force parallel to the ramp for $$6.20\ \mathrm{m}. $$What is the work done by gravity?

Accepted Answer

$$-404\ \mathrm{J}$$

Question 6

Two blocks of masses $$2\ \mathrm{kg}$$ and $$3\ \mathrm{kg}$$ are in contact on a frictionless surface. A $$15\ \mathrm{N}$$ force is applied to the $$2\ \mathrm{kg}$$ block. What is the magnitude of the force on the $$2\ \mathrm{kg}$$ block exerted by the $$3\ \mathrm{kg}$$ block?

Accepted Answer

$$9\ \mathrm{N}$$

Question 7

Two blocks of mass $$m_1$$ and $$m_2$$ ($$m_1$$ \u003e $$m_2) $$slide with the same initial speed onto a rough surface ($$\mu \u003e 0) $$and stop. Which block travels farther before stopping?

Accepted Answer

They will go the same distance.

Question 8

A $$62\ \mathrm{kg}$$ person sits on a $$4.0\ \mathrm{kg}$$ chair with four legs. Each leg contacts the floor in a circle of $$1.5\ \mathrm{cm}$$ diameter. What is the pressure exerted on the floor by each leg?

Accepted Answer

$$9.2 	imes 10^5$\ \mathrm{Pa}$$

Question 9

A $$20\ \mathrm{kg}$$ object is released from rest at the top of a frictionless $$8.0\ \mathrm{m}$$ incline at $$30^\circ. It $$slides onto a horizontal surface with $$\mu_k = 0.40$$ and stops after distance $$d. $$What is $$d$$?

Accepted Answer

$$10\ \mathrm{m}$$

Question 10

A gymnast is modeled as a uniform solid cylinder ($$m = 68.0\ \mathrm{kg}$$, $$d = 1.20\ \mathrm{m}) $$rolling at $$0.550\ \mathrm{rev/s}. $$What is the total kinetic energy?

Accepted Answer

$$219\ \mathrm{J}$$

Question 11

Superman drinks water through a straw of length $$l = 8.0\ \mathrm{m}. $$What is the water pressure at the top of the straw? ($$ho = 1000\ \mathrm{kg/m^3$}$$, $$1\ \mathrm{atm} = 1.01 	imes 10^5$\ \mathrm{Pa})$$

Accepted Answer

$$2.26 	imes 10^4$\ \mathrm{Pa}$$

Question 12

An archerfish spits water at $$60^\circ$$ above the horizontal to hit an insect $$1.8\ \mathrm{m}$$ above the water, at the highest point of the trajectory. What is the required speed?

Accepted Answer

$$6.9\ \mathrm{m/s}$$

Question 13

Which of the following is the correct dimensional analysis for $$\frac{v^2$}{a}$$, where $$[v] = L/T$$ and $$[a] = L/T^2$?

Accepted Answer

$$L$$

Question 14

A force of $$15\ \mathrm{N} is $$applied to a $$2\ \mathrm{kg}$$ block in contact with a $$3\ \mathrm{kg}$$ block on a frictionless surface. What is the acceleration of the system?

Accepted Answer

$$3\ \mathrm{m/s^2$}$$

Question 15

A $$68.0\ \mathrm{kg}$$ gymnast (modeled as a cylinder, $$d = 1.20\ \mathrm{m}) $$rolls at $$0.550\ \mathrm{rev/s}. $$What is the rotational kinetic energy? ($$I = \frac{1}{2} m R^2$)

Accepted Answer

$$55\ \mathrm{J}$$

Question 16

A $$20\ \mathrm{kg}$$ object slides down a frictionless $$8.0\ \mathrm{m}$$ incline at $$30^\circ$$ and then across a horizontal surface with $$\mu_k = 0.40. $$What is the work done by friction on the horizontal surface if it stops after $$10\ \mathrm{m}$$?

Accepted Answer

$$-784\ \mathrm{J}$$

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