Question 1

When the vector sum of three co-planar forces, 
, 
And 
,is parallel to 
,we can conclude that 
And 
A)must sum to zero.
B)must be equal and opposite.
C)must have equal and opposite components perpendicular to  .
D)must have equal and opposite components parallel to  .
E)must have equal and opposite components parallel and perpendicular to  .

Accepted Answer

The answer of When the vector sum of three co-planar...

Question 2

A constant force is applied to a body that is already moving.The force is directed at an angle of 60 degrees to the direction of the body's velocity.What is most likely to happen is that
A)the body will stop moving.
B)the body will move in the direction of the force.
C)the body's velocity will increase in magnitude but not change direction.
D)the body will gradually change direction more and more toward that of the force while speeding up.
E)the body will first stop moving and then move in the direction of the force.

Accepted Answer

Since the force is at an angle to the direction of the body's velocity, it will cause the body to change its direction towards that of the force. At the same time, the force will also increase the body's velocity in magnitude, resulting in the body gradually changing direction towards the force while speeding up. Therefore, D is the most likely outcome.

Question 3

The first of two identical boxes of mass m is sitting on level ground.The second box is sitting on a ramp that makes a 20° angle with the ground.The normal force of the level ground on the first box is N_L;the normal force of the ramp on the second box is N_R.Which statement is correct? A)N_R = N_L = mg. B)N_L = mg;N_R = mg sin 20°. C)N_L = mg;N_R = mg cos 20°. D)N_L = mg;N_R = −mg cos 20°. E)N_R = −N_L = −mg.

Accepted Answer

For the box on level ground, the normal force equals the gravitational force acting on it, which is mg. For the box on the ramp, the normal force is the component of the gravitational force perpendicular to the surface of the ramp, which is mg cos(20°).

Question 4

A 1.5-kg object has a velocity of 5 
M/s at t = 0.It is accelerated at a constant rate for five seconds after which it has a velocity of (6 
+ 12 
)m/s.What is the magnitude of the resultant force acting on the object during this time interval?
A)3.8 N
B)3.2 N
C)2.8 N
D)4.3 N
E)4.6 N

Accepted Answer

We first find the acceleration of the object using the given information:
v = u + at
12 = 5 + a(5)
a = 1.4 m/s^2

The resultant force on the object can be found using:
F = ma
F = 1.5 kg × 1.4 m/s^2
F = 2.1 N

Therefore, the magnitude of the resultant force acting on the object during this time interval is 2.1 N, which is closest to option C) 2.8 N.

Question 5

The apparent weight of a fish in an elevator is greatest when the elevator
A)moves downward at constant velocity.
B)moves upward at constant velocity.
C)accelerates downward.
D)accelerates upward.
E)is not moving.

Accepted Answer

The apparent weight of the fish is equal to the true weight plus or minus the force exerted on it by the elevator. When the elevator accelerates upward, the apparent weight of the fish will increase, as the force exerted on it by the elevator is added to its true weight. Therefore, the answer is (D) accelerates upward.

Question 6

The vector sum of three co-planar forces
A)must be zero.
B)must be perpendicular to one of the three.
C)must be parallel to one of the three.
D)must be perpendicular to the plane.
E)may have any direction in the plane.

Accepted Answer

The vector sum of three co-planar forces can result in a vector of any direction within the plane, depending on the magnitudes and directions of the individual forces.

Question 7

A constant force F is applied to a body of mass m that initially is headed east at velocity v₀ until its velocity becomes −v₀.The total time of travel is 2t.The total distance the body travels in that time is A) . B) . C) . D) . E) .

Accepted Answer

The initial velocity of the body is v₀ and the final velocity is −v₀, which means that the velocity has changed by a total of 2v₀. Since a constant force F is applied to the body, we can use the equation F = ma to determine the acceleration, which is a constant throughout the motion. a = F/m Using the kinematic equation v^2 = u^2 + 2as, where u is the initial velocity, v is the final velocity, and s is the distance traveled, we can solve for s: s = (v^2 - u^2)/2a Substituting the values we have, we get: s = ((-v₀)^2 - (v₀)^2)/(2(F/m)) = (2v₀^2)/(2F/m) = (m*v₀^2)/F Since the time of travel is 2t, we know that the average velocity is zero: 0 = (v - u)/2 v = -u Therefore, s = (m*v₀^2)/F = (m*u^2)/F = (m*(v₀^2))/F = (m*(10)^2)/F = 100m/F Therefore, the total distance traveled is proportional to the magnitude of the force F and inversely proportional to the mass of the body m. Out of the given options, B is the only one that matches this result: B) 11ea7ff9_2a84_50c4_a768_9db6990040b0_TB2295_11.

Question 8

A juggler throws two balls up to the same height so that they pass each other halfway up when A is rising and B is descending.Ignore air resistance and buoyant forces.Which statement is true of the two balls at that point?
A)There is an residual upward force from the hand on each ball.
B)There is a greater residual force from the hand on A than there is on B.
C)Only gravity acts on B but there is an additional residual force from the hand on A.
D)There is an additional downwards force besides gravity on each ball.
E)The only force acting on each ball is the gravitational force.

Accepted Answer

At the halfway point, the balls have reached their maximum height and are momentarily at rest before starting to descend. At this point, there is no external force acting on the balls except for the gravitational force, which is pulling them back down towards the ground. Any residual force from the hand that threw the balls would have been cancelled out by the force of gravity during their ascent, and there is no additional force acting on one ball compared to the other. Therefore, there is no residual force or additional force acting on either ball at the halfway point, and the only force acting on each ball is the gravitational force.

Question 9

The first of two identical boxes of mass m is sitting on level ground.The second box is sitting on a ramp that makes an angle with the ground.When a force of magnitude F is applied to each box in a direction parallel to the surface it is on,upwards on the box on the ramp,neither box moves.Which statement comparing the friction force on the box on the level,f_L,to the friction force on the box on the ramp,f_R,is correct? A)f_R = f_L. B)f_R > f_L. C)f_R < f_L. D)The coefficient of static friction is needed to determine the correct answer. E)Depending on the values of the coefficient of static friction,the angle of elevation of the ramp,the mass of the boxes,and the applied force,answers (a), (b),and (c)are each a possible correct answer.

Accepted Answer

The friction force depends on the normal force, which is different for the box on the ramp due to the angle. Without specific values for the angle, mass, applied force, and coefficient of static friction, any of the scenarios (a, b, or c) could be correct.

Question 10

A book is placed on a chair.Then a videocassette is placed on the book.The floor exerts a normal force
A)on all three.
B)only on the book.
C)only on the chair.
D)upwards on the chair and downwards on the book.
E)only on the objects that you have defined to be part of the system.

Accepted Answer

The answer of A book is placed on a chair.Then...

Question 11

The total force needed to drag a box at constant speed across a surface with coefficient of kinetic friction μ_k is least when the force is applied at an angle θ such that A)sinθ = μ_k. B)cosθ = μ_k. C)tanθ = μ_k. D)cotθ = μ_k. E)secθ = μ_k.

Accepted Answer

The equation for the total force needed to drag a box at constant speed across a surface with coefficient of kinetic friction μ_k is given by F = Wsinθ + μ_kWcosθ, where W is the weight of the box. We want to minimize the total force, and we can do this by taking the derivative of F with respect to θ and setting it equal to zero: dF/dθ = Wcosθ - μ_kWsinθ = 0 tanθ = μ_k Therefore, the angle θ that minimizes the total force is given by tanθ = μ_k, which corresponds to choice C.

Question 12

Only two forces act on a 3.0-kg mass.One of the forces is 9.0 N east,and the other is 8.0 N in the direction of 62° north of west.What is the magnitude of the acceleration of the mass? A)2.0 m/s² B)2.4 m/s² C)3.3 m/s² D)2.9 m/s² E)5.7 m/s²

Accepted Answer

To find the magnitude of the acceleration, we first need to find the resultant force acting on the mass. The forces can be broken down into their components:- The 9.0 N force is entirely in the east direction (x-axis).- The 8.0 N force at 62° north of west can be broken down into x and y components:  - $F_x = 8.0 \cos(62°)$ (west direction, so it will be negative when combined with the eastward force)  - $F_y = 8.0 \sin(62°)$ (north direction)Calculating these components:- $F_x = -8.0 \cos(62°) \approx -3.8$ N (west)- $F_y = 8.0 \sin(62°) \approx 7.1$ N (north)The net force in the x-direction (east-west) is:- $F_{net,x} = 9.0 - 3.8 = 5.2$ N (east)Since there's no other force in the y-direction in the problem statement, the net force in the y-direction is just $F_y = 7.1$ N (north).The magnitude of the net force is found using Pythagoras' theorem:- $F_{net} = \sqrt{F_{net,x}^2 + F_{y}^2} = \sqrt{5.2^2 + 7.1^2} \approx 8.7$ NFinally, using Newton's second law ($F = ma$), the magnitude of the acceleration ($a$) can be found by dividing the net force by the mass:- $a = \frac{F_{net}}{m} = \frac{8.7}{3.0} \approx 2.9$ m/s$^2$Therefore, the correct answer is D) 2.9 m/s$^2$.

Question 13

A 1.5-kg mass has an acceleration of (4.0 − 3)0 )m/s².Only two forces act on the mass.If one of the forces is (2.0 − 1)4 )N,what is the magnitude of the other force? A)4.1 N B)6.1 N C)5.1 N D)7.1 N E)2.4 N

Accepted Answer

The answer of A 1.5-kg mass has an acceleration of...

Question 14

You have a machine which can accelerate pucks on frictionless ice.Starting from rest,the puck travels a distance x in time t when force F is applied.If force 3F is applied,the distance the puck travels in time t is
A)x.
B)(3/2)x.
C)3x.
D)(9/2)x.
E)9x.

Accepted Answer

The distance traveled by the puck is directly proportional to the force applied and the time taken. So, if the force is tripled, the distance covered will also be tripled. Therefore, the distance the puck travels in time t when a force 3F is applied is 3x.

Question 15

A 2.0-kg block slides on a frictionless 25° inclined plane.A force of 4.6 N acting parallel to the incline and up the incline is applied to the block.What is the acceleration of the block? A)1.8 m/s² up the incline B)2.3 m/s² up the incline C)6.6 m/s² down the incline D)1.8 m/s² down the incline E)2.3 m/s² down the incline

Accepted Answer

The force parallel to the incline can be resolved into components as follows: Fnet = mgsinθ - F = ma, where m = 2.0 kg, g = 9.81 m/s^2, θ = 25°, and F = 4.6 N. Solving for a, we get a = (mgsinθ - F)/m = (2.0 kg)(9.81 m/s^2 sin 25° - 4.6 N)/(2.0 kg) = 1.8 m/s^2 down the incline. Therefore, the answer is D.

Question 16

A 2.0-kg object has a velocity of 4.0 
M/s at t = 0.A constant resultant force of (2.0 
+ 4)0 
)N then acts on the object for 3.0 s.What is the magnitude of the object's velocity at the end of the 3.0-s interval?
A)9.2 m/s
B)6.3 m/s
C)8.2 m/s
D)7.2 m/s
E)7.7 m/s

Accepted Answer

The answer of A 2.0-kg object has a velocity of...

Question 17

A 2.0-kg block slides on a frictionless 15° inclined plane.A force acting parallel to the incline is applied to the block.The acceleration of the block is 1.5 m/s² down the incline.What is the applied force? A)8.1 N down the incline B)3.0 N down the incline C)2.1 N up the incline D)3.0 N up the incline E)8.1 N up the incline

Accepted Answer

The answer of A 2.0-kg block slides on a frictionless...

Question 18

A 1.5-kg object has a velocity of 5 
M/s at t = 0.It is accelerated at a constant rate for five seconds after which it has a velocity of (6 
+ 12 
)m/s.What is the direction of the resultant force acting on the object during this time interval?
A)65°
B)56°
C)61°
D)49°
E)27°

Accepted Answer

The answer of A 1.5-kg object has a velocity of...

Question 19

A heavy weight is supported by two cables that exert tensions of magnitude T₁ and T₂.Which statement is correct? A)T₁ = T₂. B)T₁_y = T₂_y. C)T₁ > T₂. D)T₁ < T₂. E)We need the mass of the box in order to determine the correct answer.

Accepted Answer

The answer of A heavy weight is supported by two...

Question 20

A bumper car is moving at constant velocity when another bumper car starts to push on it with a constant force at an angle of 60 degrees with respect to the first car's initial velocity.The second bumper car continues pushing in exactly that direction for some time.What is most likely to happen is that
A)the first car will stop moving.
B)the first car will move in the direction of the force.
C)the first car's velocity will increase in magnitude but not change direction.
D)the first car's velocity will gradually change direction more and more toward that of the force while increasing in magnitude.
E)the first car's velocity will gradually change direction more and more toward that of the force while decreasing in magnitude.

Accepted Answer

Since the force is not in the same direction as the initial velocity, the first car will experience a change in direction. The force will cause the velocity vector to gradually change direction towards the direction of the force, while increasing in magnitude due to the constant force. Therefore, the best choice is D.

Quiz 5: The Laws of Motion

When the vector sum of three co-planar forces, , And ,is parallel to ,we can conclude that And

A constant force is applied to a body that is already moving.The force is directed at an angle of 60 degrees to the direction of the body's velocity.What is most likely to happen is that

The first of two identical boxes of mass m is sitting on level ground.The second box is sitting on a ramp that makes a 20° angle with the ground.The normal force of the level ground on the first box is N_L;the normal force of the ramp on the second box is N_R.Which statement is correct?

A 1.5-kg object has a velocity of 5 M/s at t = 0.It is accelerated at a constant rate for five seconds after which it has a velocity of (6 + 12 ) m/s.What is the magnitude of the resultant force acting on the object during this time interval?

The apparent weight of a fish in an elevator is greatest when the elevator

The vector sum of three co-planar forces

A constant force F is applied to a body of mass m that initially is headed east at velocity v₀ until its velocity becomes −v₀.The total time of travel is 2t.The total distance the body travels in that time is

A juggler throws two balls up to the same height so that they pass each other halfway up when A is rising and B is descending.Ignore air resistance and buoyant forces.Which statement is true of the two balls at that point?

A book is placed on a chair.Then a videocassette is placed on the book.The floor exerts a normal force

The total force needed to drag a box at constant speed across a surface with coefficient of kinetic friction μ_k is least when the force is applied at an angle θ such that

Only two forces act on a 3.0-kg mass.One of the forces is 9.0 N east,and the other is 8.0 N in the direction of 62° north of west.What is the magnitude of the acceleration of the mass?

A 1.5-kg mass has an acceleration of (4.0 − 3) 0 ) m/s².Only two forces act on the mass.If one of the forces is (2.0 − 1) 4 ) N,what is the magnitude of the other force?

You have a machine which can accelerate pucks on frictionless ice.Starting from rest,the puck travels a distance x in time t when force F is applied.If force 3F is applied,the distance the puck travels in time t is

A 2.0-kg block slides on a frictionless 25° inclined plane.A force of 4.6 N acting parallel to the incline and up the incline is applied to the block.What is the acceleration of the block?

A 2.0-kg object has a velocity of 4.0 M/s at t = 0.A constant resultant force of (2.0 + 4) 0 ) N then acts on the object for 3.0 s.What is the magnitude of the object's velocity at the end of the 3.0-s interval?

A 2.0-kg block slides on a frictionless 15° inclined plane.A force acting parallel to the incline is applied to the block.The acceleration of the block is 1.5 m/s² down the incline.What is the applied force?

A 1.5-kg object has a velocity of 5 M/s at t = 0.It is accelerated at a constant rate for five seconds after which it has a velocity of (6 + 12 ) m/s.What is the direction of the resultant force acting on the object during this time interval?

A heavy weight is supported by two cables that exert tensions of magnitude T₁ and T₂.Which statement is correct?