Q: A 2.5-kg box slides at $$1.2\ \mathrm{m/s} on a $$rough surface and compresses a spring by $$5.0\ \mathrm{cm}$$ before stopping (Image 3). If the work done by friction is $$-0.50\ \mathrm{J}$$, what is the spring constant $$k$$?

$$1.0 \times 10^3$\ \mathrm{N/m}$$

Q: A spring of unknown constant $$k is $$compressed $$0.14\ \mathrm{m} to $$launch a $$65\ \mathrm{g}$$ rocket to a height of $$35\ \mathrm{m}. $$What should $$k be$$?

$$2.3 \times 10^3$\ \mathrm{N/m}$$

Question 1

In the vector diagram shown (Image 1), which of the following correctly expresses vector $$\vec{S} in $$terms of vectors $$\vec{M}$$ and $$\vec{N}$$?

Accepted Answer

$$\vec{S} = \vec{N} - \vec{M}$$

Question 2

A car starts from rest and accelerates at $$1.50\ \mathrm{m/s^2$}$$ for $$4.00\ \mathrm{s}$$, then continues at constant velocity for $$5.00\ \mathrm{s}. $$What is the total distance traveled by the car?

Accepted Answer

$$42.0\ \mathrm{m}$$

Question 3

A 0.200-kg ball collides with a wall, changing its velocity from $$20.0\ \mathrm{m/s}$$ toward the wall to $$12.0\ \mathrm{m/s}$$ away from the wall in $$60.0\ \mathrm{ms}. $$What is the magnitude of the average force applied to the ball?

Accepted Answer

$$107\ \mathrm{N}$$

Question 4

In the two-block system shown (Image 2), a force $$2F is $$applied at $$60^\circ$$ below the horizontal to the left block ($$2m$$), and a force $$F/2 is $$applied to the right block ($$m) to $$the left. What is the acceleration of the system?

Accepted Answer

$$a = \dfrac{F - F/2}{3m}$$

Question 5

A 2.5-kg box slides at $$1.2\ \mathrm{m/s} on a $$rough surface and compresses a spring by $$5.0\ \mathrm{cm}$$ before stopping (Image 3). If the work done by friction is $$-0.50\ \mathrm{J}$$, what is the spring constant $$k$$?

Accepted Answer

$$1.0 	imes 10^3$\ \mathrm{N/m}$$

Question 6

A block of mass $$m$$ hangs from a massless cord wrapped around a uniform disk of mass $$M$$ and radius $$R ($$Image 4). What is the acceleration $$a of $$the block as it descends?

Accepted Answer

$$a = \dfrac{mg}{m + \frac{M}{2}}$$

Question 7

A 1200-kg car rounds a flat turn of radius $$81.0\ \mathrm{m}$$ with a coefficient of static friction $$\mu_s = 0.50. $$What is the maximum speed at which the car can safely make the turn?

Accepted Answer

$$20\ \mathrm{m/s}$$

Question 8

A 5.00-kg box slides $$5.00\ \mathrm{m}$$ across the floor before coming to rest. If its initial speed was $$3.00\ \mathrm{m/s}$$, what is the coefficient of kinetic friction?

Accepted Answer

$$0.092$$

Question 9

A child sleds down a frictionless hill with a vertical drop of $$7.2\ \mathrm{m}$$, then slides across a rough horizontal stretch with $$\mu_k = 0.51. $$How far does she slide on the rough stretch before stopping?

Accepted Answer

$$14.1\ \mathrm{m}$$

Question 10

A uniform disk of mass $$M$$ and radius $$R is $$mounted on a fixed axle. A block of mass $$m$$ hangs from a cord wrapped around the rim. What is the tension $$T in $$the cord as the block accelerates downward?

Accepted Answer

$$T = m(g - a)$$

Question 11

A 1000-kg car traveling west at $$10.0\ \mathrm{m/s}$$ collides with a 500-kg car traveling south at $$20.0\ \mathrm{m/s}. $$The cars stick together. What is the speed of the wreckage just after the collision?

Accepted Answer

$$9.43\ \mathrm{m/s}$$

Question 12

A 0.014-kg fragment moves at $$48\ \mathrm{m/s} in $$the $$+x$$ direction after an explosion. The second fragment moves at $$32\ \mathrm{m/s}. $$What is the mass and direction of the second fragment?

Accepted Answer

$$21\ \mathrm{g}$$, -x direction

Question 13

A spring of unknown constant $$k is $$compressed $$0.14\ \mathrm{m} to $$launch a $$65\ \mathrm{g}$$ rocket to a height of $$35\ \mathrm{m}. $$What should $$k be$$?

Accepted Answer

$$2.3 	imes 10^3$\ \mathrm{N/m}$$

Question 14

A 14,000-kg boxcar moving at $$1.50\ \mathrm{m/s}$$ couples with a stationary 10,000-kg boxcar. What is their speed just after the collision?

Accepted Answer

$$0.875\ \mathrm{m/s}$$

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