Homework Answers
The radius of curvature of the path can be calculated by using radius of curvature equation for path. The normal acceleration can be calculated if velocity and radius of curvature are known.
If the normal acceleration and tangential acceleration are known, the magnitude of the acceleration can be obtained using total acceleration equation. The direction the velocity can be calculated using slope equation of the path.
If the equation for the curve is given, without mentioning the value of radius of the curve then the radius of the curvature is calculated by radius of curvature equation.
If the body is moving in curvilinear motion, then the body has two acceleration components. One is normal acceleration and another one is tangential acceleration.
Velocity is obtained by differentiation of displacement with respect to time. Velocity is a vector quantity that means it has direction. This direction is along the tangent to the path through which the object moves.
Here, s is the distance and time is t.
The magnitude of acceleration is derived by differentiation of velocity with respect to time. Acceleration is of two components. One is tangential acceleration and other is radial acceleration. Tangential acceleration is obtained by derivative. Radial acceleration is obtained by formula.
Consider the following formulas:
Here, radius of curvature is 
.
Radius of curvature is the reciprocal of curvature. Radius of curvature for curve is the distance from center of the curve top any point on curve. It is equal to radius in case of curves.
If the path is expressed as 
, then the radius of curvature 
at any point on the path is calculated by using following expression:
The equation to calculate the magnitude of acceleration is,
Write the equation of the curve.
Differentiate the above equation with respect to x.
Differentiate the above equation with respect to x.
Let 
be the angle, the crate’s velocity is directed.
Calculate the direction of the crate’s velocity.
Substitute 
for 
and 
for x.
Calculate the radius of curvature of the path as follows:
Substitute for and 
for 
.
![(21/1)
zx[z(21/* ) +1]](http://img.homeworklib.com/questions/021b8bf0-4b0d-11ea-b8e8-df47805fdd17.png?x-oss-process=image/resize,w_560)
Substitute 
for x.
![[1+(11.2/12]]
(112)
[1.871]
(112)
= 30.7135f](http://img.homeworklib.com/questions/02d421c0-4b0d-11ea-ac7c-bd7dcb5e8caf.png?x-oss-process=image/resize,w_560)
Calculate the normal acceleration of the crate as follows:
Here, v is velocity of the crate.
Substitute 
for 
and 
for v.
Writ the tangential acceleration of the crate.
Calculate the magnitude of the crate acceleration as follows:
Substitute 
for 
and 
for 
.
The direction of the crate’s velocity is 
.
The magnitude of the crate’s acceleration is 
.
3.when x =10 ft, the crate has a speed of 20 ft/s which is increasing at...
3.when x =10 ft, the crate has a speed of 20 ft/s which is increasing at 6 ft/s^2. Determine the direction of the crate?s velocity and magnitude of crate?s acceleration at this instant.
The crate C is being lifted by moving the roller at A downward with a constant...
The crate C is being lifted by moving the roller at A downward with a constant speed of VA = 2 m/s along the guide. When the roller is at B, the crate rests on the ground. Neglect the size of the pulley in the calculation. Hint: Relate the coordinates uc and A using the problem geometry, then take the first and second time derivatives. (Figure 1) Part A Determine the magnitude of the velocity of the crate at the...
The motorcycle is traveling at 8 m/s when it is at A. The speed is then...
The motorcycle is traveling at 8 m/s when it is at A. The speed
is then increased at v? = 0.2 m/s2 .
b: determine the acceleration of the motercycle at the instant t
= 7 s
Problem 12.123 Part A The motorcycle is traveling at 8 m/s when it is at A. The speed is then increased at Determine the speed of the motorcycle at the instant t7 s Express your answer to three significant figures and include the...
Problem 12.225 Part A Cars A and B are traveling around the circular race track. At...
Problem 12.225 Part A Cars A and B are traveling around the circular race track. At the instant shown, A has a speed of 76 ft/s and is increasing its speed at the rate of 15 ft /s2, whereas B has a speed of 113 ft/s and is decreasing its speed at 25 ft /s2. (Figure 1) Determine the relative velocity of car A with respect to car B at this instant Express your answer to three significant figures and...
Problem 16.104 At a given instant the bottom A of the ladder has an acceleration a...
Problem 16.104 At a given instant the bottom A of the ladder has an acceleration a A = 4.2 ft/s2 and velocity VA = 6.2 ft/s, both acting to the left. (Figure 1) Part A Determine the acceleration of the top of the ladder, B. Express your answer to three significant figures and include the appropriate units. O": MÅR O 2 ? ab = Value Units Submit Request Answer Part B Figure < 1 of 1 > Determine the ladder's...
Problem 14.92 The roller coaster car has a speed of vA 26 ft/s when it is...
Problem 14.92 The roller coaster car has a speed of vA 26 ft/s when it is at the crest of a vertical parabolic track. The total weight of the car and the passengers is 360 lb. Neglect friction and the mass of the wheels. (Figure 1) Figure 1 of 1 x y 200 (40000-) 200 ft 200 ft Part A Determine the car's velocity when it reaches point B. Express your answer to three significant figures and include the appropriate...
At a given instant the bottom A of the ladder has an acceleration a A =...
At a given instant the bottom A of the ladder has an acceleration a A = 3.8 ft/s and velocity va = 6.4 ft/s, both acting to the left. (Figure 1) Part A Determine the acceleration of the top of the ladder, B. Express your answer to three significant figures and include the appropriate units. UA ab = Value Units Figure < 1 of 1 > Submit Request Answer Part B Determine the ladder's angular acceleration at this same instant....
Part A The center O of the gear and the gear rack P move with the velocities and accelerations sh...
Part A The center O of the gear and the gear rack P move with the velocities and accelerations shown. Assume that vo 3.4 m/s and ao 6.4 m/s2 . (Figure 1) Determine the angular acceleration of the gear at the instant shown. Express your answer to three significant figures and include the appropriate units. aValue Units Submit Part B Determine the magnitude of the acceleration of point B located at the rim of the gear at the instant shown...
When the 150-a, skier is at point a he has a speed of 5 ft/s. When...
When the 150-a, skier is at point a he has a speed of 5 ft/s. When the skier reaches point B on the smooth slope, the slope follows the cosine curve shown. Suppose that y (x) = 63 cos (x/100 x) ft. where x is in ft. Neglect friction and air resistance. Determine the skier's speed when he reaches point b on the smooth slope Express your answer to three significant figures and include the appropriate units. What is the...
Part A The motorcycle is traveling at 50 m/s when it is at A. The speed...
Part A The motorcycle is traveling at 50 m/s when it is at A. The speed is then decreased at v= -(0.05s) m/s, where s is in meters measured from A. Suppose that p= 150 m. (Figure 1) Determine the speed of the motorcycle when it reaches B. Express your answer to three significant figures and include the appropriate units. View Available Hint(s) НА ? VB = Value Units Figure < 1 of 1 > Submit -60° р Part B...
3.when x =10 ft, the crate has a speed of 20 ft/s which is increasing at 6 ft/s^2. Determine the direction of the crate?s velocity and magnitude of crate?s acceleration at this instant.
The crate C is being lifted by moving the roller at A downward with a constant speed of VA = 2 m/s along the guide. When the roller is at B, the crate rests on the ground. Neglect the size of the pulley in the calculation. Hint: Relate the coordinates uc and A using the problem geometry, then take the first and second time derivatives. (Figure 1) Part A Determine the magnitude of the velocity of the crate at the...
The motorcycle is traveling at 8 m/s when it is at A. The speed
is then increased at v? = 0.2 m/s2 .
b: determine the acceleration of the motercycle at the instant t
= 7 s
Problem 12.123 Part A The motorcycle is traveling at 8 m/s when it is at A. The speed is then increased at Determine the speed of the motorcycle at the instant t7 s Express your answer to three significant figures and include the...
Problem 12.225 Part A Cars A and B are traveling around the circular race track. At the instant shown, A has a speed of 76 ft/s and is increasing its speed at the rate of 15 ft /s2, whereas B has a speed of 113 ft/s and is decreasing its speed at 25 ft /s2. (Figure 1) Determine the relative velocity of car A with respect to car B at this instant Express your answer to three significant figures and...
Problem 16.104 At a given instant the bottom A of the ladder has an acceleration a A = 4.2 ft/s2 and velocity VA = 6.2 ft/s, both acting to the left. (Figure 1) Part A Determine the acceleration of the top of the ladder, B. Express your answer to three significant figures and include the appropriate units. O": MÅR O 2 ? ab = Value Units Submit Request Answer Part B Figure < 1 of 1 > Determine the ladder's...
Problem 14.92 The roller coaster car has a speed of vA 26 ft/s when it is at the crest of a vertical parabolic track. The total weight of the car and the passengers is 360 lb. Neglect friction and the mass of the wheels. (Figure 1) Figure 1 of 1 x y 200 (40000-) 200 ft 200 ft Part A Determine the car's velocity when it reaches point B. Express your answer to three significant figures and include the appropriate...
At a given instant the bottom A of the ladder has an acceleration a A = 3.8 ft/s and velocity va = 6.4 ft/s, both acting to the left. (Figure 1) Part A Determine the acceleration of the top of the ladder, B. Express your answer to three significant figures and include the appropriate units. UA ab = Value Units Figure < 1 of 1 > Submit Request Answer Part B Determine the ladder's angular acceleration at this same instant....
Part A The center O of the gear and the gear rack P move with the velocities and accelerations shown. Assume that vo 3.4 m/s and ao 6.4 m/s2 . (Figure 1) Determine the angular acceleration of the gear at the instant shown. Express your answer to three significant figures and include the appropriate units. aValue Units Submit Part B Determine the magnitude of the acceleration of point B located at the rim of the gear at the instant shown...
When the 150-a, skier is at point a he has a speed of 5 ft/s. When the skier reaches point B on the smooth slope, the slope follows the cosine curve shown. Suppose that y (x) = 63 cos (x/100 x) ft. where x is in ft. Neglect friction and air resistance. Determine the skier's speed when he reaches point b on the smooth slope Express your answer to three significant figures and include the appropriate units. What is the...
Part A The motorcycle is traveling at 50 m/s when it is at A. The speed is then decreased at v= -(0.05s) m/s, where s is in meters measured from A. Suppose that p= 150 m. (Figure 1) Determine the speed of the motorcycle when it reaches B. Express your answer to three significant figures and include the appropriate units. View Available Hint(s) НА ? VB = Value Units Figure < 1 of 1 > Submit -60° р Part B...
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