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Q.5 A.() If f(x,y) = 2 * sin(x+y), then prove that 2002 - (2 Marks) (ii)...
Suppose a force of 40 N is required to stretch and hold a spring 0.1 m from its equilibrium position. a. Assuming the spring obeys Hooke's law, find the spring constant k. b. How much work is req...
Suppose a force of 40 N is required to stretch and hold a spring 0.1 m from its equilibrium position. a. Assuming the spring obeys Hooke's law, find the spring constant k. b. How much work is required to compress the spring 0.2 m from its equilibrium position? c. How much work is required to stretch the spring 0.5 m from its equilibrium position? d. How much additional work is required to stretch the spring 0.1 m if it has...
(1 point) Finding the work done in stretching or compressing a spring. Hooke's Law for Springs....
(1 point) Finding the work done in stretching or compressing a spring. Hooke's Law for Springs. According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x) = kx, for some constant k. The value of k (measured in force units per unit length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive. Part 1. Suppose that it takes...
Question 15 A spring required a force of 5.0 N to compress it 0.1 m. How...
Question 15 A spring required a force of 5.0 N to compress it 0.1 m. How much work is required to stretch the spring 0.4 m? Hint: Work done is equal to the change in elastic potential energy 0.8) O 0.4) 2) 0.2
3) Consider Hooke's Law: The force required to keep a spring in a compressed or stretched position x units from the spring's equilibrium position is F(x)-kr Calculate the work required, in jo...
3) Consider Hooke's Law: The force required to keep a spring in a compressed or stretched position x units from the spring's equilibrium position is F(x)-kr Calculate the work required, in joules, to stretch a spring 0.4 meters beyond its equilibrium position for each of the following scenarios. a) The spring requires 50 Newtons of force to hold it 0.1 m from its equilibrium position. b) The spring requires 2 Joules of work to stretch the spring 0.1 meter from...
Consider a spring that does not obey Hooke's law very faithfully. One end of the spring...
Consider a spring that does not obey Hooke's law very faithfully. One end of the spring is fixed. To keep the spring stretched or compressed an amount x, a force along the x-axis with x-component Fx=kx−bx2+cx3 must be applied to the free end. Here k=100N/m, b=700N/m2, and c=12000N/m3. Note that x>0 when the spring is stretched and x<0 when it is compressed. A)How much work must be done to stretch this spring by 0.050 m from its unstretched length? B)How...
Please help with 4a and 4b 4. (8 marks) A spring of natural length L is...
Please help with 4a and 4b
4. (8 marks) A spring of natural length L is hung vertically with a mass of 2 kg attached to the end. 4(a) Assume that the friction is negligible and the spring constant is k 128. Find the position of the mass at time t, if the spring is pulled down 0.2m from its equilibrium position and released with velocity 0 at time t = 0. Flo)0.2 4(b) Assume that a spring, with an...
Need the answer as soon as possible a. Show that y = y + y2 is...
Need the answer as soon as possible
a. Show that y = y + y2 is a solution of y" + P(x)y' + Q(x)y = T (x) + T2(x) if y, and y, are the solution of the following equations respectively; y + P(x)y' + Q(x)y = Ti(x) and y" + P(x)y' + Q(x)y = T2(x) (CO2:P01 - 4 Marks) b. Determine the general solution of the given equation using method of undetermined coefficients y" +9y = 2 sin 3x...
Use Hooke's Law for this (F = - k s ): Where F is the spring's...
Use Hooke's Law for this (F = - k s ): Where F is the spring's restoring force; k is the spring constant; and s is the stretch. The negative sign means the spring's restoring force is opposite the stretch direction. You have a plot from weight [N] versus stretch [m]. The data forms a linear trend y = 3.662 * x + 1.67. How much will the spring stretch if 51.7 grams is hung on the spring? Answer in...
QUESTION 2 ITOTAL MARKS: 20)] [10 Marks] Q 2(a) An object rests on a plane parallel...
QUESTION 2 ITOTAL MARKS: 20)] [10 Marks] Q 2(a) An object rests on a plane parallel to the x-y plane. A 9 N force acting in the z-direction moves this object from the point (6,3,5) to the point (11,1,7), where distance is measured in meters. (a) Determine the force vector (b) Determine the displacement vector (c) Hence, determine the work done by the force on the object. Hint: Remember that work is a scalar quantity!
Q.3) (7 Marks An object of mass m is being acted upon by a force F(x)...
Q.3) (7 Marks An object of mass m is being acted upon by a force F(x) = Fosin (cx), where F. = 2 N and c = 0.5 rad/m are constants (a) Prove that this force is conservative. (b) Find the potential energy function V(x) (c) Make a graph of the potential energy V(x) as a functions of x in the interval [x = -a m,x = + m) d) Us previous graph to discuss the motion of the particle...
Suppose a force of 40 N is required to stretch and hold a spring 0.1 m from its equilibrium position. a. Assuming the spring obeys Hooke's law, find the spring constant k. b. How much work is required to compress the spring 0.2 m from its equilibrium position? c. How much work is required to stretch the spring 0.5 m from its equilibrium position? d. How much additional work is required to stretch the spring 0.1 m if it has...
(1 point) Finding the work done in stretching or compressing a spring. Hooke's Law for Springs. According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x) = kx, for some constant k. The value of k (measured in force units per unit length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive. Part 1. Suppose that it takes...
Question 15 A spring required a force of 5.0 N to compress it 0.1 m. How much work is required to stretch the spring 0.4 m? Hint: Work done is equal to the change in elastic potential energy 0.8) O 0.4) 2) 0.2
3) Consider Hooke's Law: The force required to keep a spring in a compressed or stretched position x units from the spring's equilibrium position is F(x)-kr Calculate the work required, in joules, to stretch a spring 0.4 meters beyond its equilibrium position for each of the following scenarios. a) The spring requires 50 Newtons of force to hold it 0.1 m from its equilibrium position. b) The spring requires 2 Joules of work to stretch the spring 0.1 meter from...
Please help with 4a and 4b
4. (8 marks) A spring of natural length L is hung vertically with a mass of 2 kg attached to the end. 4(a) Assume that the friction is negligible and the spring constant is k 128. Find the position of the mass at time t, if the spring is pulled down 0.2m from its equilibrium position and released with velocity 0 at time t = 0. Flo)0.2 4(b) Assume that a spring, with an...
Need the answer as soon as possible
a. Show that y = y + y2 is a solution of y" + P(x)y' + Q(x)y = T (x) + T2(x) if y, and y, are the solution of the following equations respectively; y + P(x)y' + Q(x)y = Ti(x) and y" + P(x)y' + Q(x)y = T2(x) (CO2:P01 - 4 Marks) b. Determine the general solution of the given equation using method of undetermined coefficients y" +9y = 2 sin 3x...
QUESTION 2 ITOTAL MARKS: 20)] [10 Marks] Q 2(a) An object rests on a plane parallel to the x-y plane. A 9 N force acting in the z-direction moves this object from the point (6,3,5) to the point (11,1,7), where distance is measured in meters. (a) Determine the force vector (b) Determine the displacement vector (c) Hence, determine the work done by the force on the object. Hint: Remember that work is a scalar quantity!
Q.3) (7 Marks An object of mass m is being acted upon by a force F(x) = Fosin (cx), where F. = 2 N and c = 0.5 rad/m are constants (a) Prove that this force is conservative. (b) Find the potential energy function V(x) (c) Make a graph of the potential energy V(x) as a functions of x in the interval [x = -a m,x = + m) d) Us previous graph to discuss the motion of the particle...
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