30. A truck of mass 2250 kg is used to pull a 330 kg trunk out of an old quarry as shown below. There is 550 N of rolling resistance for the truck. Ignore mass and friction of the pulley. (a) If the trunk is accelerated upward at 2.00 m/s2 what is the minimum amount of horizontal force the truck’s drive wheels exert on the ground? (b) For the same conditions what is the tension in the towrope?

m1=2250 kg, m2 =330 kg, R=550 N, a= 2 m/s²

m1•a=F-R-T
m2•a =T- m2•g
a(m1+m2)=F-R-T+T-m2•g
F= a(m1+m2) +m2•g+R=...
T=m2(a+g)=…

To solve this problem, we can start by calculating the net force acting on the trunk.

(a) The net force acting on the trunk is given by the equation:

Net Force = Mass * Acceleration

The mass of the trunk is 330 kg and the acceleration is 2.00 m/s^2. Substituting these values into the equation, we get:

Net Force = 330 kg * 2.00 m/s^2
= 660 N

Since the trunk is being pulled upward, the tension in the towrope must be equal to this net force acting on the trunk, which is 660 N.

(b) Now let's calculate the net force acting on the truck. The net force acting on the truck is equal to the horizontal component of the tension in the towrope, minus the rolling resistance force.

Net Force = Tension - Rolling Resistance

The rolling resistance force is given as 550 N. The tension in the towrope is the same as the net force acting on the trunk, which we calculated to be 660 N.

Net Force = 660 N - 550 N
= 110 N

Therefore, the minimum amount of horizontal force the truck's drive wheels exert on the ground is 110 N.

To find the minimum amount of horizontal force exerted by the truck's drive wheels on the ground, we need to consider the forces acting on the truck.

Let's break down the problem step by step:

(a) To calculate the minimum amount of horizontal force exerted by the truck's drive wheels on the ground, we need to consider the forces acting on the truck. The forces acting on the truck are the rolling resistance force (550 N), the force due to the truck's acceleration (ma), and the force due to the tension in the towrope (T).

From Newton's second law, we know that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:

Net force (F_net) = ma

In this case, the net force is the sum of the rolling resistance force and the force due to the truck's acceleration:

F_net = rolling resistance force + ma

Substituting the given values, we have:

F_net = 550 N + (2250 kg)(2.00 m/s^2)

Simplifying the equation, we find:

F_net = 550 N + 4500 N
F_net = 5050 N

Therefore, the minimum amount of horizontal force the truck's drive wheels exert on the ground is 5050 N.

(b) To find the tension in the towrope, we need to consider the forces acting on the trunk. The forces acting on the trunk are the force due to the truck's acceleration (ma) and the tension in the towrope (T).

Using the same approach as in part (a), we can write the equation:

F_net = ma + T

Since the trunk is being accelerated upward, the net force acting on it is equal to its mass multiplied by its acceleration:

F_net = (330 kg)(2.00 m/s^2)
F_net = 660 N

Substituting this value in the equation, we have:

660 N = (330 kg)(2.00 m/s^2) + T

Simplifying the equation, we find:

T = 660 N - 660 N
T = 0 N

Therefore, the tension in the towrope is 0 N.

(a) Well, this sounds like quite the trucking adventure! To find the minimum amount of horizontal force the truck's drive wheels exert on the ground, we can start by calculating the net force acting on the truck.

The net force can be found using Newton's second law: F_net = m_truck * a, where m_truck is the mass of the truck and a is the acceleration of the trunk.

F_net = (2250 kg) * (2.00 m/s^2) = 4500 N

Now, let's consider the rolling resistance. Rolling resistance opposes the motion of the truck and can be thought of as a negative force. So, we subtract the rolling resistance from the net force:

F_horizontal = F_net - Rolling resistance
F_horizontal = 4500 N - 550 N
F_horizontal = 3950 N

Therefore, the minimum amount of horizontal force the truck's drive wheels exert on the ground is 3950 N.

(b) Now, let's move on to finding the tension in the towrope. Since the truck is pulling the trunk, the tension in the towrope will be the same as the force exerted by the truck on the trunk.

Using Newton's second law again, we have:

Tension = m_trunk * a = (330 kg) * (2.00 m/s^2) = 660 N

So, the tension in the towrope is 660 N.

Hope that brings a little traction to your understanding!