Homework SourseAn object is traveling along the x axis with the potential e
An object is traveling along the x axis with the potential energy shown in the figure. If the object has a mass of 4.25 kg and a speed of 7.50 m/s at the origin, determine the total energy of the object, force acting on the object, acceleration of the object, and speed of the object at the following positions.
(a) x = 1.00 m
E= _____ J
F= _____ N
a= _____ m/s2
v= _____ m/s
(b) x = 3.00 m
E= _____ J
F= _____ N
a= _____ m/s2
v= _____ m/s
(c) x = 6.00 m
E= _____ J
F= _____ N
a= _____ m/s2
v= _____ m/s
8 6Solution
a)
At x = 1 m
total energy = 0.5*m*u^2
= 0.5*4.25*7.5^2
E = 119.5 J
F = dU/dx = slope
= 10/2 = 5 N
a = F/m = 5/4.25
= 1.18 m/s2
v = sqrt(2*(0.5*mu^2 - U)/m)
= sqrt(2*(0.5*4.25*7.5^2 - 5)/4.25)
= 7.34 m/s
b)
At x = 3 m
total energy = 0.5*m*u^2
= 0.5*4.25*7.5^2
E = 119.5 J
F = dU/dx = slope
= 0
a = F/m = 0
v = sqrt(2*(0.5*mu^2 - U)/m)
= sqrt(2*(0.5*4.25*7.5^2 - 10)/4.25)
= 7.18 m/s
c)
At x = 6 m
total energy = 0.5*m*u^2
= 0.5*4.25*7.5^2
E = 119.5 J
F = dU/dx = slope
= 10/4 = 2.5 N
a = F/m = 2.5/4.25 = 0.588 m/s2
v = sqrt(2*(0.5*mu^2 - U)/m)
= sqrt(2*(0.5*4.25*7.5^2 - 5)/4.25)
= 7.34 m/s
