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Chapter 1: Q23P (page 40)
A proton is located at .
(a)What is , the vector from the origin to the location of the proton?
(b)What is ?
(c)What is , the unit vector in the direction of ?
(a) The vector from the origin to the location of the proton is .
(b) The magnitude ofis.
(c) The unit vector along is .
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An object in the shape of a thin ring has radius a and mass M. A uniform sphere with mass m and radius R is placed with its center at a distance x to the right of the center of the ring, along a line through the center of the ring, and perpendicular to its plane (see Fig. E13.35). What is the gravitational force that the sphere exerts on the ring-shaped object? Show that your result reduces to the expected result when x is much larger than a.
Figure 1.55 shows several arrows representing vectors in the xy plane. (a) Which vectors have magnitudes equal to the magnitude of ? (b) Which vectors are equal to ?
Figure 1.60 shows the trajectory of a ball travelling through the air, affected by both gravity and air resistance.
Here are the positions of the ball at several successive times.
Location | t(s) | Position ( m) |
A | 0.0 | (0,0,0) |
B | 1.0 | (22.3,26.1,0) |
C | 2.0 | (40.1,38.1,0) |
a) What is the average velocity of the ball as it travels between location A and location B? b) If the ball continued to travel at the same average velocity during the next second, where would it be at the end of that second? (That is, where would it be at time t=2s )c) How does your prediction from part b) compare to the actual position of the ball at t=2s(location C)? If the predicted and the observed location of the ball are different, explain why?
Here are the positions at three different times for a bee in flight (a bee鈥檚 top speed is about 7 m/s ). (a)Between 6.3 s and 6.8 s , what was the bee鈥檚 average velocity? Be careful with signs.
(b)Between6.3 s and 7.3 s, what was the bee鈥檚 average velocity? Be careful with signs.
(c)Of the two average velocities you calculated, which is the best estimate of the bee鈥檚 instantaneous velocity at time 6.3 s ?
(d)Using the best information available, what was the displacement of the bee during the time interval from 6.3 s to 6.33 s ?
In Figurethree vectors are represented by arrows in the xyplane. Each square in the grid represents one meter. For each vector, write out the components of the vector, and calculate the magnitude of the vector.
Figure 1.56
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