Q: A $$4520\ \mathrm{kg}$$ container is held by a steel cable at $$58.0^\circ$$ from the vertical and a horizontal cable. What are the tensions $$T_1 ($$slanted cable) and $$T_2 ($$horizontal cable)?

$$T_1 = 4.43$$ \times $$10^4$$\ \mathrm{N};\ $$T_2 = 2.35$$ \times $$10^4$$\ \mathrm{N}$$

Question 1

A 90-kg genie is descending at a constant speed of $$8\ \mathrm{m/s}$$ while carrying a bag of magic balls. One ball is thrown from the bag perpendicular to the genie's path at $$6\ \mathrm{m/s} ($$relative to the genie). After $$12\ \mathrm{s}$$, the genie sees the ball bounce. How far was the genie from the ground when the ball was thrown? (Assume the genie continues descending at $$8\ \mathrm{m/s}$$ and the ball is a point mass.)

Accepted Answer

$$801.6\ \mathrm{m}$$

Question 2

A rock slides off a mountain at a $$22^\circ$$ angle below the horizontal with an initial velocity of $$6.0\ \mathrm{m/s}. $$The mountain's edge is $$13\ \mathrm{m}$$ above the ground. What is the horizontal distance from the base to where the rock lands?

Accepted Answer

$$9.6\ \mathrm{m}$$

Question 3

A thief must throw a diamond pouch to a partner $$5.0\ \mathrm{m}$$ away horizontally and $$2.0\ \mathrm{m}$$ above the thrower. What angle should the pouch be thrown to reach the partner, assuming the throw speed is $$8.0\ \mathrm{m/s}$$ and neglecting air resistance?

Accepted Answer

$$42.3^\circ$$

Question 4

A seed is fired at $$55\ \mathrm{m/s} at$$ $$54.0^\circ$$ above the horizontal. Neglecting air resistance, what are the horizontal and vertical components of velocity and acceleration at the highest point?

Accepted Answer

$$v_x = 32.3\ \mathrm{m/s};\ v_y = 0\ \mathrm{m/s};\ a_x = 0\ \mathrm{m/s^2$};\ a_y = -9.8\ \mathrm{m/s^2$}$$

Question 5

A football is kicked from a cliff at $$30\ \mathrm{m/s}$$ and $$35^\circ$$ above the horizontal. What is the angle of the ball's velocity after it has traveled $$75\ \mathrm{m}$$ horizontally?

Accepted Answer

$$-27.3^\circ$$

Question 6

Three boats of masses $$30\ \mathrm{kg}$$, $$20\ \mathrm{kg}$$, and $$10\ \mathrm{kg}$$ are pulled along a frictionless surface by a $$480\ \mathrm{N}$$ force. What are the tensions $$T_A$$ and $$T_B in $$the ropes between the boats?

Accepted Answer

$$T_A = 300.0\ \mathrm{N},\ T_B = 220.0\ \mathrm{N}$$

Question 7

A $$55.0\ \mathrm{kg}$$ crash test dummy is brought from $$60.0\ \mathrm{km/h} to $$rest by an airbag over $$1.25\ \mathrm{m}. $$What is the magnitude of the average impact force on the dummy?

Accepted Answer

$$6111\ \mathrm{N}$$

Question 8

A box is placed on a frictionless surface at the back of a pick-up truck. The truck suddenly accelerates forward. What happens to the box?

Accepted Answer

The box does not accelerate but will remain at constant velocity (at rest) until it hits the back of the pick-up.

Question 9

A $$4520\ \mathrm{kg}$$ container is held by a steel cable at $$58.0^\circ$$ from the vertical and a horizontal cable. What are the tensions $$T_1 ($$slanted cable) and $$T_2 ($$horizontal cable)?

Accepted Answer

$$T_1 = 4.43$$ 	imes $$10^4$$\ \mathrm{N};\ $$T_2 = 2.35$$ 	imes $$10^4$$\ \mathrm{N}$$

Question 10

A $$75\ \mathrm{kg}$$ bookcase is pushed with a $$250\ \mathrm{N}$$ force at $$5^\circ$$ above the horizontal. The coefficient of kinetic friction is $$0.3. $$What is the acceleration of the bookcase?

Accepted Answer

$$0.3\ \mathrm{m/s^2$}$$

Question 11

Two crates, A ($$20\ \mathrm{kg}) $$and B ($$15\ \mathrm{kg}$$), are pulled with a rope on a surface with friction coefficient $$0.15. If $$the tension between crate B and the worker is $$200\ \mathrm{N}$$ and the acceleration is $$2.5\ \mathrm{m/s^2$}$$, what is the tension in the rope between A and B?

Accepted Answer

$$140.5\ \mathrm{N}$$

Question 12

A $$50\ \mathrm{kg}$$ person rides a roller coaster with a $$60\ \mathrm{m}$$ diameter loop. What is the apparent weight at the bottom of the loop at $$25\ \mathrm{m/s}$$, and at the top at $$20\ \mathrm{m/s}$$?

Accepted Answer

$$1.5\ \mathrm{kN},\ 800\ \mathrm{N}$$

Question 13

A $$1800\ \mathrm{kg}$$ car maneuvers an $$85\ \mathrm{m}$$ radius curve banked at $$28^\circ. $$The coefficient of friction is $$1.0. $$What is the maximum safe speed to avoid sliding off?

Accepted Answer

$$65.1\ \mathrm{m/s}$$

Question 14

A $$1200\ \mathrm{kg}$$ car travels at $$14\ \mathrm{m/s}$$ around a flat curve of radius $$50\ \mathrm{m}. $$What is the minimum coefficient of friction required for the car to make the turn?

Accepted Answer

$$0.375$$

Question 15

A person with a height of $$1.72\ \mathrm{m} is $$centrifuged at the end of a $$7.50\ \mathrm{m}$$ arm to $$9g. $$What is the required revolutions per minute (RPM) to achieve this acceleration?

Accepted Answer

$$1.87\ \mathrm{RPM}$$

Question 16

A $$3.5\ \mathrm{kg}$$ block compresses a spring by $$25\ \mathrm{cm}. $$What is the spring constant $$k$$?

Accepted Answer

$$429\ \mathrm{N/m}$$

Question 17

A $$5.0\ \mathrm{kg}$$ block is connected to a $$1.5\ \mathrm{kg}$$ block over a frictionless pulley. What is the acceleration of the upper box?

Accepted Answer

$$2.3\ \mathrm{m/s^2$}$$

Question 18

A $$1000\ \mathrm{kg}$$ block rests on a $$20^\circ$$ incline. If the coefficient of static friction is $$0.87$$, what is the friction force experienced by the block?

Accepted Answer

$$3532\ \mathrm{N}$$

Physics Exam Practice: Mechanics, Forces, and Motion

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