Repeat Problem 87, now generalizing to the case where not only the speed but also the radius may be changing. 87. In dealing with nonuniform circular motion, as shown in Fig. 3.23, we should write Equation 3.16 as a r = v 2 / r , to show that this is only the radial component of the acceleration. Recognizing that v is the object’s speed, which changes only in the presence of tangential acceleration, differentiate this equation with respect to time to find a relation between the magnitude of the tangential acceleration and the rate of change of the magnitude of the radial acceleration. Assume the radius stays constant.
Repeat Problem 87, now generalizing to the case where not only the speed but also the radius may be changing. 87. In dealing with nonuniform circular motion, as shown in Fig. 3.23, we should write Equation 3.16 as a r = v 2 / r , to show that this is only the radial component of the acceleration. Recognizing that v is the object’s speed, which changes only in the presence of tangential acceleration, differentiate this equation with respect to time to find a relation between the magnitude of the tangential acceleration and the rate of change of the magnitude of the radial acceleration. Assume the radius stays constant.
Repeat Problem 87, now generalizing to the case where not only the speed but also the radius may be changing.
87. In dealing with nonuniform circular motion, as shown in Fig. 3.23, we should write Equation 3.16 as ar = v2/r, to show that this is only the radial component of the acceleration. Recognizing that v is the object’s speed, which changes only in the presence of tangential acceleration, differentiate this equation with respect to time to find a relation between the magnitude of the tangential acceleration and the rate of change of the magnitude of the radial acceleration. Assume the radius stays constant.
How would I begin to solve this problem?
In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for a rocket's position measured from the center of the Earth is given by
y(t) = (RE3/2 + 3*(g/2)1/2 REt)2/3
where RE is the radius of the Earth (6.38 ✕ 106 m) and g is the constant acceleration of an object in free fall near the Earth's surface (9.81 m/s2).
(a) Derive expressions for vy(t) and ay(t). (Use the following as necessary: g, RE, and t. Do not substitute numerical values; use variables only.)
To anticipate the dip and the hump in the road, the driver of a car applies his brakes to produce a uniform deceleration. His speed is
100kph at the bottom A of the dip and 50 kph at the top Cof the hump. The length of the road from A to Cis 120m. The radius of
curvature of the hump at C is 150m. The total acceleration at A is 3 m/s^2.
Compute the radius of curvature at A.
C
60 m
В
60 m
A
A) 612.15m
B) 502.39m
c) 432.32m
D 243.23m
E) 549.81m
A particle describes an UCM(uniform circular motion) with period 0.500 s and circle centered at the origin of the x and y coordinate system.
Let î and ȷ be the unit vectors along the x and y directions, respectively.
At instant t=0 the particle's acceleration vector (in m/s2) is a =2.30î.
What is its acceleration vector (in m/s2) at time t=2.50 s?
Chapter 3 Solutions
Essential University Physics: Volume 1 (3rd Edition)
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