Question 1

A 50.0-kg crate is being pulled along a horizontal smooth surface.The pulling force is 10.0 N and is directed 20.0° above the horizontal.What is the magnitude of the acceleration of the crate?

Accepted Answer

The horizontal component of the force, which is responsible for the acceleration, is calculated as $F \cos(\theta) = 10.0 \cos(20.0^\circ)$. The acceleration $a$ is given by Newton's second law, $a = \frac{F}{m}$, where $F$ is the net force and $m$ is the mass. Substituting the horizontal force and the mass of the crate, $a = \frac{10.0 \cos(20.0^\circ)}{50.0} \approx 0.188 \, \text{m/s}^2$.

Question 2

A projectile is fired from ground level on a horizontal plain.If the initial speed of the projectile is now doubled,and we neglect air,

Accepted Answer

The range of a projectile launched with initial speed $v$ at an angle $\theta$ to the horizontal is given by the formula $R = \frac{v^2}{g} \sin 2\theta$, where $g$ is the acceleration due to gravity. If the initial speed is doubled, the new range becomes $R' = \frac{(2v)^2}{g} \sin 2\theta = 4 \frac{v^2}{g} \sin 2\theta$, which is four times the original range. Hence, the range quadruples.

Question 3

A projectile is thrown upward at 24° with the vertical and returns to the horizontal ground 12.5 s later.Assume no air effects.
(a)How fast was it thrown?
(b)How far from its original position did it land?
(c)How high above its original position did it go?

Accepted Answer

The answer of A projectile is thrown upward at 24°...

Question 4

Calculate the average force an outside object would have to exert to bring a 1200-kg car to rest in 15 cm when the car had an initial speed of 2.0 m/s (about 4.5 mph).

Accepted Answer

To find the average force, we can use the work-energy principle. The work done by the force is equal to the change in kinetic energy of the car. The initial kinetic energy (KE) of the car is given by $ \frac{1}{2}mv^2 $, where $ m = 1200 \, \text{kg} $ and $ v = 2.0 \, \text{m/s} $. The final kinetic energy is 0 (since the car comes to rest). The work done (W) is also equal to the force (F) times the distance (d), where $ d = 15 \, \text{cm} = 0.15 \, \text{m} $. Thus, we have:$$ W = \Delta KE = \frac{1}{2}mv^2 - 0 = \frac{1}{2} \times 1200 \times (2.0)^2 = 2400 \, \text{J} $$$$ W = F \times d $$$$ 2400 = F \times 0.15 $$$$ F = \frac{2400}{0.15} = 16000 \, \text{N} = 1.6 \times 10^4 \, \text{N} $$

Question 5

A 1000-kg barge is being towed by means of two horizontal cables.One cable is exerting a force of 80.0 N in a direction 30.0° west of north.In what direction should the second cable pull so that the barge will accelerate northward,if the force exerted by the cable is 120 N? Assume that the water exerts no appreciable frictional drag on the barge.

Accepted Answer

The correct answer is A because the second cable should pull in a direction 19.5° east of north to counteract the force of the first cable and accelerate the barge northward.

Question 6

A projectile is fired from the edge of a cliff as shown in the figure.The initial velocity components are 940 m/s (horizontal)and 96 m/s (vertical).The projectile reaches maximum height at point P and then falls and strikes the ground at point Q.How high is point P above point Q,assuming no air effects?

Accepted Answer

First, we can find the time it takes for the projectile to reach its maximum height using the vertical component of its initial velocity. 
vf = vi + at 
0 = 96 + (-9.8)t 
t = 9.8 seconds

We can then find the maximum height using the vertical component of position at this time. 
y = vi*t + 1/2at^2 
y = 96(9.8) + 1/2(-9.8)(9.8)^2 
y = 470.4 meters

Finally, we can find the horizontal distance traveled by the projectile using the horizontal component of its initial velocity and the time it takes to fall to the ground, which is twice the time it took to reach the maximum height. 
x = vixt 
x = 940(2*9.8) 
x = 18,412 meters

Therefore, the height of point P above point Q is 470.4 meters.

Question 7

A 958-N rocket is coming in for a vertical landing.It starts with a downward speed of 25 m/s and must reduce its speed to 0 m/s in 8.0 s for the final landing.
(a)During this landing maneuver,what must be the thrust force exerted on the rocket by the expelled gas??
(b)What must be the direction of the engine thrust force?

Accepted Answer

The answer of A 958-N rocket is coming in for...

Question 8

A 590-kg rocket is at rest on the launch pad.What upward thrust force is needed to accelerate the rocket uniformly to an upward speed of 28 m/s in 3.3 s?

Accepted Answer

The answer of A 590-kg rocket is at rest on...

Question 9

A projectile is launched with an initial velocity of 80 m/s at 30° above the horizontal.Neglecting air,what is horizontal component of the projectile's acceleration?

Accepted Answer

The horizontal component of a projectile's acceleration is always zero, since there is no force acting in the horizontal direction (assuming negligible air resistance). The only force acting on the projectile is its weight, which acts vertically downward and causes the projectile to accelerate downward at a rate of 9.8 m/s^2. However, this acceleration has no horizontal component. Therefore, choice D is the correct answer.

Question 10

A boy kicks a football with an initial velocity of 20 m/s at an angle of 25° above the horizontal.If we neglect air,the magnitude of the acceleration of the ball while it is in flight is

Accepted Answer

Since air resistance is neglected, the only acceleration acting on the ball is the acceleration due to gravity, which is 9.8 m/s$^2$ downward. The initial velocity of the ball has a horizontal component of 20cos(25°) m/s and a vertical component of 20sin(25°) m/s. The horizontal component of the velocity remains constant during the flight, and the vertical component is affected only by gravity. Therefore, the magnitude of the acceleration of the ball while it is in flight is equal to the magnitude of the acceleration due to gravity, which is 9.8 m/s$^2$.

Question 11

A car of mass 1100 kg that is traveling at 27 m/s starts to slow down and comes to a complete stop in 578 m.What is the magnitude of the average stopping force exerted on the car?

Accepted Answer

The work done to stop the car is equal to the change in kinetic energy, which can be calculated using the formula $ \Delta KE = \frac{1}{2}mv^2 $, where $ m $ is the mass of the car and $ v $ is its initial velocity. Plugging in the given values, $ \Delta KE = \frac{1}{2} \times 1100 \times 27^2 = 400950 $ Joules. The work done is also equal to the force times the distance over which it is applied, $ W = F \times d $. Rearranging for $ F $, we get $ F = \frac{W}{d} = \frac{400950}{578} \approx 693.6 $ N, which rounds to 690 N, indicating the magnitude of the average stopping force.

Question 12

A 30.0-kg load is being held in place using massless wires in the ideal pulley arrangement shown in the figure.What is the magnitude of the force F?

Accepted Answer

The answer of A 30.0-kg load is being held in...

Question 13

A 40-kg box is being pushed along a horizontal smooth surface.The pushing force is 15 N directed at an angle of 15° below the horizontal.What is the magnitude of the acceleration of the crate?

Accepted Answer

The answer of A 40-kg box is being pushed along...

Question 14

As shown in the figure,a projectile is fired at time t = 0.00 s,from point 0 at the upper edge of a cliff,with initial velocity components of $v_{ 0 x} = 30 \mathrm {~m} / \mathrm { s }$ and $v_{ 0 y} = 300 \mathrm {~m} / \mathrm { s }$ The projectile rises and then falls into the sea at point P.The time of flight of the projectile is $75.0 \mathrm {~s} ,$ and air effects are negligible.At this location,g = 9.80 m/s².What is the horizontal distance D?

Accepted Answer

The answer of As shown in the figure,a projectile is...

Question 15

A box of mass 72 kg is at rest on a horizontal frictionless surface.A constant horizontal force of magnitude F then is exerted on the box,accelerating it to the right.You observe that it takes the box 3.4 seconds to travel 13 meters.What is the magnitude of the force F?

Accepted Answer

The answer of A box of mass 72 kg is...

Question 16

Two forces are exerted on a $55 - \mathrm { kg }$ object.One force has magnitude 65 N directed 59° clockwise from the positive x-axis,and the other has a magnitude 35 N at 32° clockwise from the positive y-axis.Assuming no other forces,what is the magnitude of this object's acceleration?

Accepted Answer

To find the acceleration, first resolve each force into its x and y components. Then, sum the components to find the net force in each direction. Use the net force and the object's mass to find acceleration using $ F = ma $. The net force magnitude is approximately 60.5 N, leading to an acceleration of $ \frac{60.5}{55} \approx 1.1 \, \text{m/s}^2 $.

Question 17

A certain aircraft has a mass of 300,000 kg.At a certain instant during its landing,its speed is 27.0 m/s.If the stopping force exerted on the airplane is a constant 445,000 N,what is the speed of the airplane 10.0 s later?

Accepted Answer

The deceleration can be calculated using Newton's second law: a = F/m = 445,000 N / 300,000 kg = 1.4833 m/s². The speed after 10 seconds is v = u + at = 27.0 m/s - 1.4833 m/s² * 10 s = 12.167 m/s, approximately 12.2 m/s.

Question 18

Three forces are exerted on an object and as a result the object moves with a constant velocity.One force is 60.0 N along the +x-axis,and the second is 75.0 N along the +y-axis.What is the magnitude of the third force?

Accepted Answer

The answer of Three forces are exerted on an object...

Question 19

A hobbyist launches a projectile from ground level on a horizontal plain.It reaches a maximum height of 72.3 m and lands 111 m from the launch point.Assume no air.What was the angle of launch if g = 9.80 m/s²?

Accepted Answer

The correct answer is A because the projectile reaches its maximum height when the vertical component of its velocity is zero. The horizontal component of its velocity is constant throughout its flight. The range of the projectile is the horizontal distance it travels before landing. The angle of launch can be calculated using the following equation:$$	heta = 	an^{-1} \left(\frac{2h}{R}ight)$$where h is the maximum height and R is the range. Plugging in the given values, we get:$$	heta = 	an^{-1} \left(\frac{2(72.3 m)}{111 m}ight) = 69.0°$$

Question 20

What is the magnitude of the sum of the forces that is required to accelerate a 1200-kg car uniformly from 0 m/s to 27.0 m/s in 10.0 s?

Accepted Answer

We can use the formula:

F = m * a

where 
F = sum of the forces 
m = mass of the car = 1200 kg 
a = acceleration = (change in velocity) / time = (27.0 m/s - 0 m/s) / 10.0 s = 2.70 m/s^2

Substituting the values:

F = 1200 kg * 2.70 m/s^2 = 3240 N

Therefore, the magnitude of the sum of the forces required to accelerate the car uniformly is 3240 N. 
So, the best answer choice is C.

Quiz 4: Applying Newtons Laws

A 50.0-kg crate is being pulled along a horizontal smooth surface.The pulling force is 10.0 N and is directed 20.0° above the horizontal.What is the magnitude of the acceleration of the crate?

A projectile is fired from ground level on a horizontal plain.If the initial speed of the projectile is now doubled,and we neglect air,

A projectile is thrown upward at 24° with the vertical and returns to the horizontal ground 12.5 s later.Assume no air effects. (a)How fast was it thrown? (b)How far from its original position did it land? (c)How high above its original position did it go?

Calculate the average force an outside object would have to exert to bring a 1200-kg car to rest in 15 cm when the car had an initial speed of 2.0 m/s (about 4.5 mph) .

A 590-kg rocket is at rest on the launch pad.What upward thrust force is needed to accelerate the rocket uniformly to an upward speed of 28 m/s in 3.3 s?

A projectile is launched with an initial velocity of 80 m/s at 30° above the horizontal.Neglecting air,what is horizontal component of the projectile's acceleration?

A boy kicks a football with an initial velocity of 20 m/s at an angle of 25° above the horizontal.If we neglect air,the magnitude of the acceleration of the ball while it is in flight is

A car of mass 1100 kg that is traveling at 27 m/s starts to slow down and comes to a complete stop in 578 m.What is the magnitude of the average stopping force exerted on the car?

A 30.0-kg load is being held in place using massless wires in the ideal pulley arrangement shown in the figure.What is the magnitude of the force F?

A 40-kg box is being pushed along a horizontal smooth surface.The pushing force is 15 N directed at an angle of 15° below the horizontal.What is the magnitude of the acceleration of the crate?

A box of mass 72 kg is at rest on a horizontal frictionless surface.A constant horizontal force of magnitude F then is exerted on the box,accelerating it to the right.You observe that it takes the box 3.4 seconds to travel 13 meters.What is the magnitude of the force F?

Two forces are exerted on a $55 - \mathrm { kg }$ object.One force has magnitude 65 N directed 59° clockwise from the positive x-axis,and the other has a magnitude 35 N at 32° clockwise from the positive y-axis.Assuming no other forces,what is the magnitude of this object's acceleration?

A certain aircraft has a mass of 300,000 kg.At a certain instant during its landing,its speed is 27.0 m/s.If the stopping force exerted on the airplane is a constant 445,000 N,what is the speed of the airplane 10.0 s later?

Three forces are exerted on an object and as a result the object moves with a constant velocity.One force is 60.0 N along the +x-axis,and the second is 75.0 N along the +y-axis.What is the magnitude of the third force?

A hobbyist launches a projectile from ground level on a horizontal plain.It reaches a maximum height of 72.3 m and lands 111 m from the launch point.Assume no air.What was the angle of launch if g = 9.80 m/s²?

What is the magnitude of the sum of the forces that is required to accelerate a 1200-kg car uniformly from 0 m/s to 27.0 m/s in 10.0 s?

Quiz 4: Applying Newtons Laws

A 50.0-kg crate is being pulled along a horizontal smooth surface.The pulling force is 10.0 N and is directed 20.0° above the horizontal.What is the magnitude of the acceleration of the crate?

A projectile is fired from ground level on a horizontal plain.If the initial speed of the projectile is now doubled,and we neglect air,

A projectile is thrown upward at 24° with the vertical and returns to the horizontal ground 12.5 s later.Assume no air effects. (a)How fast was it thrown? (b)How far from its original position did it land? (c)How high above its original position did it go?

Calculate the average force an outside object would have to exert to bring a 1200-kg car to rest in 15 cm when the car had an initial speed of 2.0 m/s (about 4.5 mph) .

A 590-kg rocket is at rest on the launch pad.What upward thrust force is needed to accelerate the rocket uniformly to an upward speed of 28 m/s in 3.3 s?

A projectile is launched with an initial velocity of 80 m/s at 30° above the horizontal.Neglecting air,what is horizontal component of the projectile's acceleration?

A boy kicks a football with an initial velocity of 20 m/s at an angle of 25° above the horizontal.If we neglect air,the magnitude of the acceleration of the ball while it is in flight is

A car of mass 1100 kg that is traveling at 27 m/s starts to slow down and comes to a complete stop in 578 m.What is the magnitude of the average stopping force exerted on the car?

A 30.0-kg load is being held in place using massless wires in the ideal pulley arrangement shown in the figure.What is the magnitude of the force F?

A 40-kg box is being pushed along a horizontal smooth surface.The pushing force is 15 N directed at an angle of 15° below the horizontal.What is the magnitude of the acceleration of the crate?

A box of mass 72 kg is at rest on a horizontal frictionless surface.A constant horizontal force of magnitude F then is exerted on the box,accelerating it to the right.You observe that it takes the box 3.4 seconds to travel 13 meters.What is the magnitude of the force F?

A certain aircraft has a mass of 300,000 kg.At a certain instant during its landing,its speed is 27.0 m/s.If the stopping force exerted on the airplane is a constant 445,000 N,what is the speed of the airplane 10.0 s later?

Three forces are exerted on an object and as a result the object moves with a constant velocity.One force is 60.0 N along the +x-axis,and the second is 75.0 N along the +y-axis.What is the magnitude of the third force?

A hobbyist launches a projectile from ground level on a horizontal plain.It reaches a maximum height of 72.3 m and lands 111 m from the launch point.Assume no air.What was the angle of launch if g = 9.80 m/s2?

What is the magnitude of the sum of the forces that is required to accelerate a 1200-kg car uniformly from 0 m/s to 27.0 m/s in 10.0 s?

A hobbyist launches a projectile from ground level on a horizontal plain.It reaches a maximum height of 72.3 m and lands 111 m from the launch point.Assume no air.What was the angle of launch if g = 9.80 m/s²?