Q: A $$70.0\ \mathrm{kg}$$ astronaut pushes to the left on a spacecraft with a force $$F in$$ 'gravity-free' space. The spacecraft has a total mass of $$1.0 \times 10^4$\ \mathrm{kg}. $$During the push, the astronaut accelerates to the right with an acceleration of $$0.36\ \mathrm{m/s^2$}. $$Determine the magnitude of the acceleration of the spacecraft.

$$2.5 \times 10$$^{-2}$$\ \mathrm{m/s^2$}$$

Question 1

A baseball is hit upward and travels along a parabolic arc before it strikes the ground. Which of the following statements is necessarily true?

Accepted Answer

The acceleration of the ball is $$9.8\ \mathrm{m/s^2$}$$ when the ball is at the highest point in the arc.

Question 2

A tennis ball is thrown from ground level with velocity $$v_0$$ directed $$30^\circ$$ above the horizontal. If it takes the ball $$1.0\ \mathrm{s} to $$reach the top of its trajectory, what is the magnitude of the initial velocity?

Accepted Answer

$$11.3\ \mathrm{m/s}$$

Question 3

A projectile is fired at an angle of $$60.0^\circ$$ above the horizontal with an initial speed of $$30.0\ \mathrm{m/s}. $$What is the magnitude of the horizontal component of the projectile's displacement at the end of $$2\ \mathrm{s}$$?

Accepted Answer

$$50\ \mathrm{m}$$

Question 4

How long does it take the projectile to reach the highest point in its trajectory if it is fired at $$60.0^\circ$$ above the horizontal with an initial speed of $$30.0\ \mathrm{m/s}$$?

Accepted Answer

$$2.7\ \mathrm{s}$$

Question 5

A ball is thrown and is caught by the receiver $$2.55\ \mathrm{s}$$ later. Determine the distance the ball was thrown if its horizontal velocity was $$20\ \mathrm{m/s}.$$

Accepted Answer

$$51\ \mathrm{m}$$

Question 6

A spring-loaded gun is aimed horizontally and is used to launch identical balls with different initial speeds. If the speed of the second ball fired is twice the speed of the first ball fired, how is the horizontal range affected?

Accepted Answer

The range of the second ball will be four times as large as that of the first ball.

Question 7

A football is kicked at an angle $$	heta$$ with respect to the horizontal. Which one of the following statements best describes the acceleration of the football during this event if air resistance is neglected?

Accepted Answer

The acceleration is $$9.8\ \mathrm{m/s^2$} at $$all times.

Question 8

A $$70.0\ \mathrm{kg}$$ astronaut pushes to the left on a spacecraft with a force $$F in$$ 'gravity-free' space. The spacecraft has a total mass of $$1.0 	imes 10^4$\ \mathrm{kg}. $$During the push, the astronaut accelerates to the right with an acceleration of $$0.36\ \mathrm{m/s^2$}. $$Determine the magnitude of the acceleration of the spacecraft.

Accepted Answer

$$2.5 	imes 10$$^{-2}$$\ \mathrm{m/s^2$}$$

Question 9

A $$2.00\ \mathrm{kg}$$ projectile is fired at an angle of $$20.0^\circ. $$What is the magnitude of the force exerted on the projectile when it is at its highest position in its trajectory? Neglect any effects of air resistance.

Accepted Answer

$$19.6\ \mathrm{N}$$

Question 10

A $$4.8\ \mathrm{kg}$$ block is set moving with an initial speed of $$6\ \mathrm{m/s} on a $$rough horizontal surface. If the force of friction is $$12\ \mathrm{N}$$, approximately how far does the block travel before it stops?

Accepted Answer

$$3\ \mathrm{m}$$

Question 11

A $$10\ \mathrm{kg}$$ block is at rest on a rough inclined plane. The coefficient of static friction between the block and the wall is $$0.60$$, and the coefficient of kinetic friction is $$0.40. $$Which one of the following statements is true, if the block is initially at rest?

Accepted Answer

The block will remain at rest because the coefficient of static friction is greater than the coefficient of kinetic friction.

Question 12

A block is at rest on a rough inclined plane and is connected to an object with the same mass as shown. The rope may be considered massless; and the pulley may be considered frictionless. The coefficient of static friction between the block and the plane is $$\mu_s$$, and the coefficient of kinetic friction is $$\mu_k. $$What is the magnitude of the static frictional force acting on the block?

Accepted Answer

$$mg(1 - \sin 	heta)$$

Question 13

A block is pulled at constant speed along a rough level surface by a rope that makes an angle of $$30^\circ$$ with respect to the horizontal. The applied force along the rope is $$\vec{F}. $$The force of kinetic friction between the block and the surface is $$10\ \mathrm{N}. $$Which one of the following expressions gives the magnitude of the force $$\vec{F} in SI $$units?

Accepted Answer

$$10/\cos 30^\circ$$

Question 14

A $$4.5\ \mathrm{kg}$$ block rests on a frictionless surface. Two forces act on it as shown: $$3.7\ \mathrm{N} to $$the right and $$1.2\ \mathrm{N} to $$the left. What is the magnitude of the horizontal acceleration of the block?

Accepted Answer

$$0.82\ \mathrm{m/s^2$}$$

Question 15

A shell is fired with a horizontal velocity in the positive $$x$$ direction from the top of an $$80\ \mathrm{m}$$ high cliff. The shell strikes the ground $$1330\ \mathrm{m}$$ from the base of the cliff. What was the initial speed of the shell?

Accepted Answer

$$82\ \mathrm{m/s}$$

Question 16

A $$5\ \mathrm{kg}$$ block is at rest on a rough horizontal surface. A force of $$15\ \mathrm{N} is $$applied to the scale at the right, as shown. What is the reading on the middle scale?

Accepted Answer

$$10\ \mathrm{N}$$

Fundamental Concepts in Introductory Physics: Kinematics, Dynamics, and Forces

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