Concept explainers
The ratio of the weight of the twin in the boat to the weight of his brother on solid ground.
Answer to Problem 74P
The ratio of the weight of the twin in the boat to the weight of his brother on solid ground is
Explanation of Solution
Write the expression for the density of the lake.
Here,
Write the expression for the density of Earth.
Here,
Write the expression for the force due to lake on the twin.
Here,
Write the expression for the force due to Earth on the twin.
Here,
Use equation (II) and (I) to solve for the ratio of force of gravity due to the lake on the twin to the Earth acting on the twin.
Use equation (V) to solve for the
Write the expression for
Here,
Use equation (VII) to write the expression for the
Use equation (VIII) in (I) to solve for
Use equation (IX) and (VII) in (IV) to solve for
Write the expression for the difference in the force due to Earth to the lake acting on the twins.
Here,
Write the expression for the ratio of total weight experienced by the twins.
Use equation (XI) in (XII) to solve for
Conclusion:
Substitute
Substitute
Substitute
Therefore, the ratio of the weight of the twin in the boat to the weight of his brother on solid ground is
Want to see more full solutions like this?
Chapter 5 Solutions
College Physics, Volume 1
- You are holding a basketball and standing at rest on top of a skateboard. If you throw the basketball (of mass 0.625 kg) at a velocity of 7 m/s along the horizontal and you and the skateboard together have a mass of 85 kg, what is the magnitude of your velocity just after throwing the ball? Assume you can ignore air resistance, rolling resistance, and friction.arrow_forwardIndividual masses on a line Sketch the following system on a number line and find the location of the center of mass. m1 = 8 kg located at x = 2 m; m2 = 4 kg located at x = -4 m;m3 = 1 kg located at x = 0 marrow_forwardAn asteroid has a mass of m = 8.5 × 1012 kg and also has two rocket thrusters attached to it. One thruster supplies a force with x- and y- componentsF 1 = (8.0 × 107, 7.0 × 107) N while the other supplies a force with x- and y-components F 2 = (4.0 × 107, −2.0 × 107) N. (You may ignore the mass of the rocket thrusters and their fuel.)- What is the magnitude of the resultant force and in which direction does it act?arrow_forward
- A bag of cement weighing 325 N hangs in equilibrium from three wires as suggested in Figure P4.23. Two of the wires make angles 1 = 60.0 and 2 = 40.0 with the horizontal. Assuming the system is in equilibrium, find the tensions T1, T2, and T3 in the wires. Figure P4.23 Problems 23 and 24.arrow_forwardTo lift off from the Moon, a 9.50 105 kg rocket needs a thrust larger than the force of gravity. If the exhaust velocity is 4.25 103 m/s, at what rate does the exhaust need to be expelled to provide sufficient thrust? The acceleration due to gravity on the Moon is 1.62 m/s2.arrow_forwardTwo telephone poles are separated by 40 m and connected by a wire. A bird of mass 0.5 kg lands on the wire midway between the poles, causing the wire to sag 2 m below horizontal. Assuming the wire has negligible mass, what is the tension in the wire?arrow_forward
- The two tugboats apply the forces P and Q to the barge, where P=76 kN and Q=52 kN. Determine the resultant of P and Q.arrow_forwardDuring the filming of a certain movie scene, the director wants a small car (whose mass is m1) traveling due east at speed v1 to collide with a small truck (whose mass is m2) traveling north. The director also wants the collision to be arranged so that just afterward, the interlocked vehicles travel straight toward the camera. If the line between the camera and collision makes an angle of theta with respect to north, at what speed v2 should the trucker drive?arrow_forwardA 6100 kg rocket is set for vertical firing from the ground. If the exhaust speed is 1200 m/s, how much gas must be ejected each second if the thrust (a) is to equal the magnitude of the gravitational force on the rocket and (b) is to give the rocket an initial upward acceleration of 21 m/s2?arrow_forward
- One of the first ion engines on a commercial satellite used Xenon as a propellant and could eject the ionized gas at a rate of 2.98 ✕ 10−6 kg/s with an exhaust speed of 3.04 ✕ 104 m/s. What instantaneous thrust (in N) could the engine provide? (Enter your answer to at least three significant figures. Enter the magnitude.)arrow_forwardThere are two forces on the 1.19 kg box in the overhead view of the figure but only one is shown. For F1 = 15.7 N, a = 14.7 m/s2, and θ = 34.1°, find the second force (a) in unit-vector notation and as (b) a magnitude and (c) a direction. (State the direction as a negative angle measured from the +x direction.)arrow_forwardA system of three particles with masses m1 = 3.0 kg, m2 = 4.0 kg and m3 = 8.0 kg is placed on a two dimensional xy plane. The scales on the axes are set by xs = 2.0 m and ys = 2.0 m. (a) Find out the x coordinate of the system’s center of mass.(b) Find out the y coordinate of the system’s center of mass.(c) Find out the acceleration of the system if an external force of 5 N acts on it.arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning