Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force of 75.0 N, the second a force of 90.0 N, friction is 12.0 N, and the mass of the third child plus wagon is 23.0 kg.
(a) What is the system of interest if the acceleration of the child in the wagon is to be calculated?
(b) Draw a free-body diagram, including all forces acting on the system.
(c) Calculate the acceleration.
(d) What would the acceleration be if friction were 15.0 N?
(a) The system here is the child inside the wagon along with the wagon.
(b) The free-body diagram is drawn as shown below.
(c) The value of acceleration is 0.13 m/s2.
(d) The value of acceleration will be zero.
For calculating the acceleration of the child inside the wagon, the system would be the child inside the wagon along with the wagon.
Draw the free-body diagram of the system along with the forces acting on it as shown below,
Here, W is the weight of the wagon plus the child, F1 is the force exerted by the first child, F2 is the force applied by the second child, f is the friction force, N is the normal reaction, m is the mass of wagon plus the third child.
Apply Newton’s second law of motion.
Here, Fnet is the net force, and a is the acceleration.
Substitute 75N for F1, 90N for F2, 12N for f, and 23kg for m in equation (i), and we get,
Hence, the value of the acceleration is 0.13 m/s2.
Substitute 75N for F1, 90N for F2, 15N for f, and 23kg for m in equation (i), and we get,
Hence, the acceleration will be 0.
What is the ratio of the strength of the strong nuclear force to that of the electromagnetic force? Based on this ratio, you might expect that the strong force dominates the nucleus, which is true for small nuclei. Large nuclei, however, have sizes greater than the range of the strong nuclear force. At these sizes, the electromagnetic force begins to affect nuclear stability. These facts will be used to explain nuclear fusion and fission later in this text.
Two teams of nine members each engage in a tug of war. Each of the first team’s members has an average mass of 68 kg and exerts an average force of 1350 N horizontally. Each of the second team’s members has an average mass of 73 kg and exerts an average force of 1365 N horizontally.
(a) What is magnitude of the acceleration of the two teams?
(b) What is the tension in the section of rope between the teams?
Commercial airplanes are sometimes pushed out of the passenger loading area by a tractor.
(a) An 1800-kg tractor exerts a force of 1.75×104 N backward on the pavement, and the system experiences forces resisting motion that total 2400 N. If the acceleration is 0.150 m/s2, what is the mass of the airplane?
(b) Calculate the force exerted by the tractor on the airplane, assuming 2200 N of the friction is experienced by the airplane.
(c) Draw two sketches showing the systems of interest used to solve each part, including the free-body diagrams for each.
In Figure 4.7, the net external force on the 24-kg mower is stated to be 51 N. If the force of friction opposing the motion is 24 N, what force F (in newtons) is the person exerting on the mower? Suppose the mower is moving at 1.5 m/s when the force F is removed. How far will the mower go before stopping?
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