progress check a
A moon orbits a planet in a nearly circular orbit of radius R, as shown in the figure. The moon has a mass of 1×1022 kg, and the gravitational field strength at a distance R from the planet is 0.001 N/kg. What is the gravitational force exerted on the moon while it is in orbit around the planet?
1×10^19 N
A moon of mass 1×1020 kg is in a circular orbit around a planet. The planet exerts a gravitational force of 2×1021 N on the moon. The centripetal acceleration of the moon is most nearly
20 m/8 squared
Two containers of water can have their individual masses varied by adding or removing water. The containers are initially a distance dd apart, as measured from their centers, and are filled with water so that each has a mass MM, as shown in Figure 1 above. The gravitational force that one container exerts on the other is F0F0. Water is then added to one container so that its mass increases to 1.5M1.5M, and water is removed from the other container so that its mass decreases to 0.5M0.5M, as shown in Figure 2. What is the new gravitational force exerted on one container by the other?
3/4F0
A 2 kg object is released from rest near the surface of a planet with a negligible atmosphere. A graph of the object's speed v as a function of time t is shown. What is the weight of the object on the planet?
8 N
A scientist designs an experiment that requires two atomic particles whose only fundamental force exerted between them is the gravitational force. Which combination of particles and separation distance will meet this condition?
A proton and neutron located 1.0 mm apart
A student must determine the inertial mass of a block attached to a horizontal track. The block is free to move horizontally along the track, as shown above. Frictional forces are considered to be negligible. The student may only choose two measuring tools to determine the inertial mass of the block. What tools should the student choose? Select two answers.
Accelerometer and Force sensor
In which of the following situations is the gravitational force the dominant force? Select two answers.
An object is in free fall just after it is released from rest. AND A satellite is in orbit around a planet
Two experiments are conducted are conducted to determine the mass of an object. In Experiment 1, the object's weight is measured by using an electronic balance once the object has been placed at rest on the balance. In Experiment 2, the object is pulled along a horizontal surface with a spring scale such that the force reading on the spring scale remains constant while a motion detector is used to measure the instantaneous speed of the object as it is pulled. All frictional forces for both experiments are considered to be negligible. Which of the two experiments, if either, could be used to determine the gravitational mass of the object?
Experiment 1 only
A moon orbits a planet in a nearly circular orbit of radius R, as shown in the figure. Which of the following free-body diagrams could be used to analyze the forces exerted on the moon when it is at the position indicated in the figure?
FGRAVITY arrow pointed to the right
Planet X has a mass of MM and a radius of RR. Planet Y has a mass of 3M3M and a radius of 3R3R. Identical satellites orbit both planets at a distance RR above their surfaces, as shown above. The planets are separated by such a large distance that the gravitational forces between them are negligible. How does the magnitude of the gravitational force FYFY exerted by Planet Y on its satellite compare to the gravitational force FXFX exerted by Planet X on its satellite?
FY=3/4 FX
An Atwood machine is placed on a planet in which the acceleration due to gravity on the planet is unknown. Both ends of a light string are attached to two blocks such that M1>M2M1>M2 , and the string passes through a pulley such that frictional forces are considered to be negligible, as shown above. The same tension force TT is exerted on both blocks, and the block of mass M1M1 experiences an acceleration a0a0 in the downward direction when released from rest. Which quantities would allow the acceleration due to gravity on the planet to be determined?
M1M1 , M2M2 , and a0
A rocket on Earth experiences an upward applied force from its thrusters. As a result of this force, the rocket accelerates upward at 2 m/s22 m/s2. Assume that there are no other upward forces exerted on the rocket and that wind resistance is negligible. Which of the following combinations of the rocket's mass mRocketmRocket and force from its thrusters FThrustersFThrusters would result in an upward acceleration of 2 m/s22 m/s2? Select two answers.
MRocket:3kg FThrusters:36N ALSO MRocke:t1kg FThrusters:12N
A student must conduct two experiments so that the inertial mass and gravitational mass of the same object can be determined. In the experiment to find the object's gravitational mass, the student ties one end of a string around the object with the other end tied to a spring scale so that the object can vertically hang at rest. In the experiment to find the object's inertial mass, the student uses a spring scale to pull the object, starting from rest, across a horizontal surface with a constant applied force such that frictional forces are considered to be negligible. In addition to the spring scale, the student has access to other measuring devices commonly found in a science laboratory. Which of the following lists the essential measuring devices the student can use to collect the data necessary to find the object's gravitational and inertial mass?
Meterstick and timer
PositionTangential Speed (m/s)A3.16B5.46C7.07D5.46 Student X ties one end of a string to a 0.5 kg ball and swings the ball in a vertical circle of radius 1 m, as shown in the figure. Student Y uses video analysis to determine the speed of the ball at points A, B, C, and D, as shown in the table. Student X states that the data are incorrect because the tension in the string provides a centripetal force that should cause the ball to travel with a constant tangential speed. Is Student X's reasoning correct, and why or why not?
No, because the net centripetal force exerted on the ball is the combination of the tension force from the string and the force due to gravity from Earth.
A student uses a motion sensor to collect data about an object's velocity v as a function of time t after it is released from rest near Earth's surface. The student claims that the graph shown represents the object while in free fall. Does the data from the graph support the student's claim?
No, because the slope of the curve of the graph indicates that the acceleration is less than gg, which indicates that a force other than gravity is exerted on the object.
Item 6 An object is placed on a rotating disk. The amount of time it takes the object to make one revolution around the center of the circle may be set at a known value. Which of the following procedures could be used to make the necessary measurements to find the coefficient of static friction between the object and the disk's surface?
Place the object on the disk and measure the distance from the center of the disk to the center of mass of the object by using a meterstick. Slowly increase the rate the disk rotates until the object begins to slide off the disk. Record the time in which the object makes one revolution around the center of the disk.
A ball of Mass MM is swung in a vertical circle with a constant tangential speed. Figure 1 shows the forces exerted on the ball at the top of the circle, and Figure 2 shows the forces exerted on the ball at the bottom of the circle. Which of the following is an expression for the centripetal acceleration of the ball in terms of MM, T1T1, T2T2, and any fundamental constants?
T1+T2/2M
A student analyzes data of the motion of a planet as it orbits a star that is in deep space. The orbit of the planet is considered to be stable and does not change over time. The student claims, "The only experimentally measurable external force exerted on the planet is the force due to gravity from the star." Is the student's claim supported by the evidence? What reasoning either supports or contradicts the student's claim?
Yes. Other external forces are exerted on the planet, but they are of negligible magnitude.
Satellite AA orbits a planet at a distance dd from the planet's center with a centripetal acceleration a0a0. A second identical satellite BB orbits the same planet at a distance 2d2d from the planet's center with centripetal acceleration abab. What is the centripetal acceleration abab in terms of a0a0 ?
a0/4
Planet X has a mass of MM and a radius of RR. Planet Y has a mass of 3M3M and a radius of 3R3R. Identical satellites orbit both planets at a distance RR above their surfaces, as shown above. The planets are separated by such a large distance that the gravitational forces between them are negligible. How does the gravitational field gXgX at the surface of Planet X compare with the gravitational field gYgY at the surface of Planet Y?
gX=3gY
An object of mass M is placed on a disk that can rotate. One end of a string is tied to the object while the other end of the string is held by a pole that is located at the center of the disk. Initially, the object is spun in a horizontal circle of radius R at a constant tangential speed of v0, as shown in the figure, such that the tension in the string is T. At a later time, the disk is spun such that the tangential speed of the object is increased to 2v0 . At a later time, the tangential speed of the object is increased to 3v0 . Which of the following diagrams could represent the forces exerted on the object at one of the given speeds? Assume that the force of static friction is negligible. Select two answers.
graph labeled 4T and graph labeled 9T
