Find the scalar product of the vectors in Figure P7.10.
The scalar product of the two vectors is 5.33 J.
Magnitude of the first vector
A =32.8 N
Magnitude of the second vector
Large angle made by the first vector and y axis =
Large angle made by the second vector and x axis =
The dot product of two vectors and is
Large angle between the positive y axis and the positive x axis =
Thus, angle between the two vectors
From equation (I), the dot product of the two vectors is
Thus the required dot product is 5.33 J.
Figure P6.57 shows a photo of a swing ride at an amusement park. The structure consists of a horizontal, rotating, circular platform of diameter D from which seats of mass m are suspended at the end of mass less chains of length d. When the system rotates at constant speed, the chains swing outward and make an angle with the vertical. Consider such a ride with the following parameters: D = 8.00 m, d = 2.50 m, m = 10.0 kg , and = 28.0 (a) What is the speed of each seat? (b) Draw a diagram of forces acting on the combination of a seat and a 40.0 - kg child and (c) find tension in the chain.
Galileo thought about whether acceleration should be defined as the rate of change of velocity over time or as the rate of change in velocity over distance. He chose the former, so let's use the name "vroomosity" for the rate of change of velocity over distance. For motion of a particle on a straight line with constant acceleration, the equation gives its velocity v as a function of time. Similarly, for a particle's linear motion with constant vroomosity k , the equation gives the velocity v as a function of the position x if the particle's speed is at x = 0 . (a) Find the law describing the total force acting on this object of mass m. (b) Describe an example of such a motion or explain why it is unrealistic. Consider (c) the possibility of k positive and (d) the possibility of k negative.
A surveyor measures the distance across a straight river by the following method (Fig. P3.7). Starting directly across from a tree on the opposite bank, she walks d=100m along the riverbank to establish a baseline. Then she sights across to the tree. The angle from her baseline to the tree is . How wide is the river?
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