Math / Algebra

QuestionIn the figure, an airport luggage carrying train with a tractor (T) is pulling three luggage carts, $M_1$ , $M_2$ , and $M_3$ , with constant velocity of $4.5$ m/s. If $T = 50$ kg, $M_1 = 40$ kg, $M_2 = 15$ kg, and $M_3 = 10$ kg (there is no friction), then the force in the connection between the tractor (T) and cart $M_1$ is:

Studdy Solution

STEP 1

What is this asking? How strong is the pull between the tractor and the first cart if the whole train is moving at a steady speed? Watch out! Don't get tricked by all the numbers!
Constant velocity means zero acceleration.

STEP 2

1. Visualize the forces
2. Calculate the total mass being pulled
3. Find the force

STEP 3

Imagine the train moving at a constant speed.
That means the tractor is pulling just hard enough to keep everything moving at $4.5$ m/s.
No speeding up, no slowing down!

STEP 4

The tractor (T) is pulling all the carts ( $M_1$ , $M_2$ , and $M_3$ ).
The force between T and $M_1$ is what's keeping those carts moving.

STEP 5

The tractor is pulling $M_1$ , $M_2$ , and $M_3$ .
Let's add those masses together to find the total mass being pulled by the tractor.

STEP 6

$\text{Total Mass} = M_1 + M_2 + M_3$ $\text{Total Mass} = 40 \text{ kg} + 15 \text{ kg} + 10 \text{ kg}$ $\text{Total Mass} = \mathbf{65} \text{ kg}$ So, the tractor is pulling a total of 65 kg of carts!

STEP 7

Since the train is moving at a constant velocity, the net force is zero!
This means the force the tractor exerts is perfectly balanced by other forces (in this case, there are no other forces since we're told there's no friction).
Newton's second law tells us: $F = ma$ .

STEP 8

Since the velocity is constant, the acceleration ( $a$ ) is zero. $F = m \cdot a$ $F = 65 \text{ kg} \cdot 0 \frac{\text{m}}{\text{s}^2}$ $F = \mathbf{0} \text{ N}$

STEP 9

The net force acting on the entire train is zero, but we're looking for the force between the tractor (T) and the first cart ( $M_1$ ).
This force is what's pulling the carts $M_1$ , $M_2$ , and $M_3$ .

STEP 10

Since the net force on the three carts is also zero, the force between the tractor and $M_1$ must be zero.

STEP 11

The force in the connection between the tractor (T) and cart $M_1$ is $\mathbf{0} \text{ N}$ .

Was this helpful?

Studdy Solution

STEP 1

What is this asking? How strong is the pull between the tractor and the first cart if the whole train is moving at a steady speed? Watch out! Don't get tricked by all the numbers!
Constant velocity means zero acceleration.

STEP 2

1. Visualize the forces
2. Calculate the total mass being pulled
3. Find the force

STEP 3

Imagine the train moving at a constant speed.
That means the tractor is pulling just hard enough to keep everything moving at $4.5$ m/s.
No speeding up, no slowing down!

STEP 4

The tractor (T) is pulling all the carts ( $M_1$ , $M_2$ , and $M_3$ ).
The force between T and $M_1$ is what's keeping those carts moving.

STEP 5

The tractor is pulling $M_1$ , $M_2$ , and $M_3$ .
Let's add those masses together to find the total mass being pulled by the tractor.

STEP 6

$\text{Total Mass} = M_1 + M_2 + M_3$ $\text{Total Mass} = 40 \text{ kg} + 15 \text{ kg} + 10 \text{ kg}$ $\text{Total Mass} = \mathbf{65} \text{ kg}$ So, the tractor is pulling a total of 65 kg of carts!

STEP 7

Since the train is moving at a constant velocity, the net force is zero!
This means the force the tractor exerts is perfectly balanced by other forces (in this case, there are no other forces since we're told there's no friction).
Newton's second law tells us: $F = ma$ .

STEP 8

Since the velocity is constant, the acceleration ( $a$ ) is zero. $F = m \cdot a$ $F = 65 \text{ kg} \cdot 0 \frac{\text{m}}{\text{s}^2}$ $F = \mathbf{0} \text{ N}$

STEP 9

The net force acting on the entire train is zero, but we're looking for the force between the tractor (T) and the first cart ( $M_1$ ).
This force is what's pulling the carts $M_1$ , $M_2$ , and $M_3$ .

STEP 10

Since the net force on the three carts is also zero, the force between the tractor and $M_1$ must be zero.

STEP 11

The force in the connection between the tractor (T) and cart $M_1$ is $\mathbf{0} \text{ N}$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

What is this asking? How strong is the pull between the tractor and the first cart if the whole train is moving at a steady speed? Watch out! Don't get tricked by all the numbers!Constant velocity means *zero* acceleration.

STEP 2

1. Visualize the forces2. Calculate the total mass being pulled3. Find the force

STEP 3

Imagine the train moving at a constant speed.That means the tractor is pulling just hard enough to keep everything moving at 4.54.54.5 m/s.No speeding up, no slowing down!

STEP 4

The tractor (T) is pulling *all* the carts (M1M_1M1​, M2M_2M2​, and M3M_3M3​).The force between T and M1M_1M1​ is what's keeping those carts moving.

STEP 5

The tractor is pulling M1M_1M1​, M2M_2M2​, and M3M_3M3​.Let's add those masses together to find the **total mass** being pulled by the tractor.

STEP 6

STEP 7

Since the train is moving at a *constant* velocity, the **net force** is *zero*!This means the force the tractor exerts is perfectly balanced by other forces (in this case, there are no other forces since we're told there's no friction).Newton's second law tells us: F=maF = maF=ma.

STEP 8

Since the velocity is constant, the acceleration (aaa) is **zero**. F=m⋅a F = m \cdot a F=m⋅a F=65 kg⋅0ms2 F = 65 \text{ kg} \cdot 0 \frac{\text{m}}{\text{s}^2} F=65 kg⋅0s2m​F=0 N F = \mathbf{0} \text{ N} F=0 N

STEP 9

The **net force** acting on the *entire* train is zero, but we're looking for the force *between* the tractor (T) and the first cart (M1M_1M1​).This force is what's pulling the carts M1M_1M1​, M2M_2M2​, and M3M_3M3​.

STEP 10

Since the net force on the three carts is also zero, the force between the tractor and M1M_1M1​ must be zero.

STEP 11

The force in the connection between the tractor (T) and cart M1M_1M1​ is 0 N\mathbf{0} \text{ N}0 N.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? How strong is the pull between the tractor and the first cart if the whole train is moving at a steady speed? Watch out! Don't get tricked by all the numbers!
Constant velocity means zero acceleration.

1. Visualize the forces
2. Calculate the total mass being pulled
3. Find the force

Imagine the train moving at a constant speed.
That means the tractor is pulling just hard enough to keep everything moving at $4.5$ m/s.
No speeding up, no slowing down!

The tractor (T) is pulling all the carts ( $M_1$ , $M_2$ , and $M_3$ ).
The force between T and $M_1$ is what's keeping those carts moving.

The tractor is pulling $M_1$ , $M_2$ , and $M_3$ .
Let's add those masses together to find the total mass being pulled by the tractor.

Since the train is moving at a constant velocity, the net force is zero!
This means the force the tractor exerts is perfectly balanced by other forces (in this case, there are no other forces since we're told there's no friction).
Newton's second law tells us: $F = ma$ .

Since the velocity is constant, the acceleration ( $a$ ) is zero. $F = m \cdot a$ $F = 65 \text{ kg} \cdot 0 \frac{\text{m}}{\text{s}^2}$ $F = \mathbf{0} \text{ N}$

The net force acting on the entire train is zero, but we're looking for the force between the tractor (T) and the first cart ( $M_1$ ).
This force is what's pulling the carts $M_1$ , $M_2$ , and $M_3$ .

Since the net force on the three carts is also zero, the force between the tractor and $M_1$ must be zero.

The force in the connection between the tractor (T) and cart $M_1$ is $\mathbf{0} \text{ N}$ .