Exam 4: Force and Newtons Laws of Motion

Two masses are connected by a string which passes over a pulley with negligible mass and friction. One mass hangs vertically and one mass slides on a 30.0 degree incline. The inclined surface has a coefficient of kinetic friction of 0.200 . The vertically hanging mass is $4.00 \mathrm{~kg}$ and the mass on the incline is $6.00 \mathrm{~kg}$ . The magnitude of the acceleration of the $4.00 \mathrm{~kg}$ mass is (the initial velocity of the $6.00 \mathrm{~kg}$ mass is down the incline)

A tractor $\mathrm{T}$ is pulling a trailer $\mathrm{M}$ with a constant velocity. If the velocity is $20 \mathrm{~m} / \mathrm{s}$ and $\mathrm{M}=200 \mathrm{~kg}$ and $\mathrm{T}=$ $500 \mathrm{~kg}$ , then the force on the trailer due to the tractor is (assume there is no friction or air resistance)

An object travels $7.5 \mathrm{~m} / \mathrm{s}$ toward the west. Under the influence of a constant net force of $5.2 \mathrm{kN}$ , after $4.3 \mathrm{~s}$ , it is travelling $2.5 \mathrm{~m} / \mathrm{s}$ toward the east. What is its mass?

Two masses are suspended by a cord that passes over a pulley with negligible mass. The cord also has negligible mass. One of the masses, $m_{1}$ , has a mass of $7.0 \mathrm{~kg}$ and the other mass, $m_{2}$ , has a mass of $3.0 \mathrm{~kg}$ . The pulley turns on a shaft through the center of the pulley, which supports the pulley and all the masses. The vertical force of the shaft on the pulley is

A box rests on a frictionless countertop. A boy pushes horizontally to the right on the box, and a girl pushes on it to the left, yet it remains stationary. Which of the following statements is false?

A tractor of mass $M_{1}=2,000 \mathrm{~kg}$ is pulling a trailer of mass $M_{2}=5,000 \mathrm{~kg}$ . If the tractor-trailer is accelerated at $2.0 \mathrm{~m} / \mathrm{s}^{2}$ , and air resistance is negligible, then the tension in the trailer hitch that connects the trailer to the tractor is

A freight train consists of an engine and several identical cars on a straight, level track. Which of the following statements is true?

An object with a mass of $200.0 \mathrm{~kg}$ is $500.0 \mathrm{~km}$ above the surface of the Earth. The magnitude of the force of gravity on the $200.0 \mathrm{~kg}$ mass is $\left(\mathrm{G}=6.67 \times 10-11 \mathrm{~N} \mathrm{~m}^{2} / \mathrm{kg}^{2}\right.$ , the radius of the Earth is $6.38 \times 10^{6} \mathrm{~m}$ , and the mass of the Earth is $5.98 \times 1024 \mathrm{~kg}$ )

A large massive rock is in contact with the Earth. Draw a force diagram for the rock and the Earth. Which of the following statements is true?

An $80.0 \mathrm{~kg}$ person is riding in an elevator that is accelerating at $2.40 \mathrm{~m} / \mathrm{s}^{2}$ downward. The apparent weight of the $80.0 \mathrm{~kg}$ person measured on a scale in the elevator is

A tractor $\mathrm{T}$ is pulling a trailer $\mathrm{M}$ with a constant acceleration. If the forward acceleration is $1.5 \mathrm{~m} / \mathrm{s}^{2}$ and $\mathrm{M}=$ $400 \mathrm{~kg}$ and $\mathrm{T}=500 \mathrm{~kg}$ , then the force on the tractor due to the trailer is (ignore air resistance)

A tractor $T$ is pulling a trailer $M$ with a constant acceleration. If the forward acceleration is $0.50 \mathrm{~m} / \mathrm{s}^{2}$ and $M$ $=400 \mathrm{~kg}$ and $\mathrm{T}=500 \mathrm{~kg}$ , then the horizontal force on the tractor due to the ground is (ignore air resistance)

The gravitational field at the Moon due to the Earth is approximately ( $\mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \mathrm{~m}^{2} / \mathrm{kg}^{2}$ , the mass of the Earth is $5.98 \times 10^{24} \mathrm{~kg}$ , and the distance to the Moon is $3.85 \times 10^{8} \mathrm{~m}$ )

A tractor of mass $M_{1}=2,000 \mathrm{~kg}$ is pulling a trailer of mass $M_{2}=5,000 \mathrm{~kg}$ . If the tractor-trailer is accelerated at $2.0 \mathrm{~m} / \mathrm{s}^{2}$ , and air resistance is negligible, then the magnitude of the force the tractor applies to the road is

A rope is connected to a spring scale on the left and exerts a force $T_{1}$ . Another rope is connected to the scale on the right and exerts a force $T_{2}$ . The scale shows a reading of $T_{s}=120 \mathrm{~N}$ . The values of $T_{1}$ and $T_{2}$ are

A tractor $T$ is pulling two trailers, $M_{1}$ and $M_{2}$ , with a constant acceleration. $T$ has a mass of $200 \mathrm{~kg}, M_{1}$ has a mass of $100 \mathrm{~kg}$ , and $M_{2}$ has a mass of $150 \mathrm{~kg}$ . If the forward acceleration is $0.60 \mathrm{~m} / \mathrm{s}^{2}$ , then the horizontal force on the tractor due to the ground is (ignore air resistance)

What is the gravitational force between two nuclei, each of mass $3.20 \times 10^{-27} \mathrm{~kg}$ , which are separated by a distance of $1.06 \times 10-10 \mathrm{~m} ?\left(\mathrm{G}=6.67 \times 10-11 \mathrm{~N} \mathrm{~m}^{2} / \mathrm{kg}^{2}\right)$

In 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 $4.5 \mathrm{~m} / \mathrm{s}$ . Unfortunately, the wheels on the carts have locked up and are sliding rather than rolling. If $T=300.0 \mathrm{~kg}, M_{1}=200.0 \mathrm{~kg}, M_{2}=100.0 \mathrm{~kg}$ , and $M_{3}=100.0 \mathrm{~kg}$ , and the coefficient of kinetic friction for each is 0.4000 , what is the force in the connection between the tractor $\mathrm{T}$ and cart $\mathrm{M}_{1}$ ? Use $\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}$ .

The gravitational field at the Earth due to the Moon is about ( $\mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \mathrm{~m}^{2} / \mathrm{kg}^{2}$ , the mass of the Moon is $7.35 \times 10^{22} \mathrm{~kg}$ , and the distance to the Moon is $3.85 \times 10^{8} \mathrm{~m}$ )

Within a given system, the internal forces